I just got an Airport Extreme (APE) and have been doing some research. I've seen a lot of questions and bits of info spread out around here. To get right to point, here's what (I think) I know:
Radio Mode! or "Your network is only as fast as the slowest device connected."
These settings can be found in Manual Setup/Airport/Wireless:
Normally the Radio Mode menu will show something like this:
However, if you hold down the OPTION key while selecting the menu you will get quite a few more choices:
It's a lot of data already, but it’s not hard! Here’s a breakdown:
802.11(x)
For starters, an 802.11g network will slow down to accommodate an 802.11b device. The same goes for an "n" network when a “g” device or less is connected. However, the degradation of speed experienced from that is far less significant than when either of those devices are connected to an "n" network. This is where a dual band router like the current APE come in. It can have two separate signals so specific devices can be on their own band, and won’t slow down the others.
What option you set will determine your network. The outdated “a” (described below) most likely won’t slow down the “n” band, and “b/g” on the other band won’t have a huge effect on each other as described above.
Frequency (GHz)
The higher the frequency, the shorter the wavelength. The shorter the wavelength, the less efficient it is at penetrating objects like walls and whatnot. "n" was made to function in the 5GHz range, however, for backwards compatibility it also supports 2.4GHz (“b/g”). Even though the range is overall smaller with 5GHz (as the same power that is used to push out 2.4GHz is the same to push out the higher 5GHz signal. I don’t know if the APE does this different than other routers), it has a far less chance to be interfered with from other signals. Furthermore, if you live in an apartment complex or a densely populated city, the 5GHz frequency also has far more channels to work with (less clutter, see below).
•“So what do I do?”•
That’s up to you to decide! For most people with notebooks, phones, and/or a newer desktop, I would recommend, “802.11n only (5GHz) - 802.11b/g/n". If you are within the 5GHz range, you will get the most out of your "n" device. If you travel outside of it, your device will connect to the 2.4GHz frequency. If it's the only device connected, it will still benefit from the "n" speeds, but again, that band will slow down if other "b/g" devices are connected at the same time (which otherwise won't happen on the "n" only 5GHz band of course). This setup would have both the advantages of a dual band network and disadvantages of a single band depending on your range.
If you will always have "b/g" devices connected to the 2.4GHz band (like I do) then setting it “802.11n only (5GHz) - 802.11b/g/" would be essentially the same.
If you have mixed devices, but can't afford the range loss of the 5GHz, set it to “802.11a/n - 802.11b/g". If you only have a couple devices, and not many visiting devices to your network, set it to whatever suits them best.
If there are several signals crowding your area, or if you live in a small apartment/house, or if you just want to get the most out of your "n" router then operate it in the 5GHz range. Personally, the 5GHz frequency has about half the distance of the 2.4GHz in my house, but the few times I go outside that range it automatically connects to the 2.4GHz network.
Enabling the 5GHz band! or "1.21 'jigawatts'?!?"
Now, to actually use the 5GHz band, you need to head to:
Once there, simply select the 5GHz network option and give it a name!
Once you do that, you’ll find the new network name in your Airport menu.
As a side note, if you want a notebook to default to this network when in the area, head into your System Preferences->Network and click the Advanced button, and just drag the preferred network to the top of the list so that if both are in range, it will connect to the 5GHz by default:
“Couldn’t you have just said that from the beginning instead of wasting my time?”
NO! I enjoy this. Expect more, or just skim through it!
Radio Channel Selection or “I can’t think of anything clever for this one.”
If there are many other routers or devices on the same frequency, this lets you tweak it ever so slightly to reduce interference. Automatic should choose the least crowded one if possible.
•“So what do I do?”•
Manually setting it for the 2.4GHz frequency could help connection problems when several wireless devices or networks exist. I would say manually changing it for the 5GHz frequency isn’t necessary unless you have those cordless phones that use the same frequency and you experience connection issues. Otherwise not many things utilize this frequency. I suggest Automatic.
Wireless Security! or “Can’t you hear me knockin’?”
WEP (Transitional Security Network) - 13 character password compatible with WPA/WPA2 devices. Original standard (with the added “transitional” technology on the APE), not easy to remember, and has been found to be more easily compromised than WPA protection.
WPA - (option not available by itself in the APE settings) - Simple explanation: Pre-standard version of ASCII password protection for networks using 8-63 characters by default.
WPA2 - (802.11i) - Official standard for WiFi protection that uses better encryption than WPA.
WPA/WPA2 - Together at last for compatibility with older devices.
•“So what do I do?”•
If in doubt, use WPA/WPA2. If you have an old or “simple” device (Nintendo DS/DSi, cell phone, Windows pre-XP SP2) it might require a WEP password or none at all.
After seeing your APE settings, you might be asking yourself, "What the hell is 802.11a?" Well, "a" came out around the same time as "b", but unlike "b" it operated on the 5GHz frequency. At the time it was more expensive than "b", had some launch problems, wasn't really successful on the consumer side, and therefore was/is mainly used with businesses. Chances are good that you will never use it.
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These are the basics I feel that I see the most questions about. If people like this, I will definitely add more information (port mapping, multicast rate, guest networking, DHCP reservations and the like) as soon as I can.
Edit: This is also my first guide, so I hope it's fairly easy to understand for people, and that the information is correct for the most part. I'm still learning myself
Radio Mode! or "Your network is only as fast as the slowest device connected."
These settings can be found in Manual Setup/Airport/Wireless:

Normally the Radio Mode menu will show something like this:

However, if you hold down the OPTION key while selecting the menu you will get quite a few more choices:

It's a lot of data already, but it’s not hard! Here’s a breakdown:
802.11(x)
For starters, an 802.11g network will slow down to accommodate an 802.11b device. The same goes for an "n" network when a “g” device or less is connected. However, the degradation of speed experienced from that is far less significant than when either of those devices are connected to an "n" network. This is where a dual band router like the current APE come in. It can have two separate signals so specific devices can be on their own band, and won’t slow down the others.
What option you set will determine your network. The outdated “a” (described below) most likely won’t slow down the “n” band, and “b/g” on the other band won’t have a huge effect on each other as described above.
Frequency (GHz)
The higher the frequency, the shorter the wavelength. The shorter the wavelength, the less efficient it is at penetrating objects like walls and whatnot. "n" was made to function in the 5GHz range, however, for backwards compatibility it also supports 2.4GHz (“b/g”). Even though the range is overall smaller with 5GHz (as the same power that is used to push out 2.4GHz is the same to push out the higher 5GHz signal. I don’t know if the APE does this different than other routers), it has a far less chance to be interfered with from other signals. Furthermore, if you live in an apartment complex or a densely populated city, the 5GHz frequency also has far more channels to work with (less clutter, see below).
•“So what do I do?”•
That’s up to you to decide! For most people with notebooks, phones, and/or a newer desktop, I would recommend, “802.11n only (5GHz) - 802.11b/g/n". If you are within the 5GHz range, you will get the most out of your "n" device. If you travel outside of it, your device will connect to the 2.4GHz frequency. If it's the only device connected, it will still benefit from the "n" speeds, but again, that band will slow down if other "b/g" devices are connected at the same time (which otherwise won't happen on the "n" only 5GHz band of course). This setup would have both the advantages of a dual band network and disadvantages of a single band depending on your range.
If you will always have "b/g" devices connected to the 2.4GHz band (like I do) then setting it “802.11n only (5GHz) - 802.11b/g/" would be essentially the same.
If you have mixed devices, but can't afford the range loss of the 5GHz, set it to “802.11a/n - 802.11b/g". If you only have a couple devices, and not many visiting devices to your network, set it to whatever suits them best.
If there are several signals crowding your area, or if you live in a small apartment/house, or if you just want to get the most out of your "n" router then operate it in the 5GHz range. Personally, the 5GHz frequency has about half the distance of the 2.4GHz in my house, but the few times I go outside that range it automatically connects to the 2.4GHz network.
Enabling the 5GHz band! or "1.21 'jigawatts'?!?"
Now, to actually use the 5GHz band, you need to head to:

Once there, simply select the 5GHz network option and give it a name!

Once you do that, you’ll find the new network name in your Airport menu.

As a side note, if you want a notebook to default to this network when in the area, head into your System Preferences->Network and click the Advanced button, and just drag the preferred network to the top of the list so that if both are in range, it will connect to the 5GHz by default:

“Couldn’t you have just said that from the beginning instead of wasting my time?”
NO! I enjoy this. Expect more, or just skim through it!
Radio Channel Selection or “I can’t think of anything clever for this one.”
If there are many other routers or devices on the same frequency, this lets you tweak it ever so slightly to reduce interference. Automatic should choose the least crowded one if possible.
•“So what do I do?”•
Manually setting it for the 2.4GHz frequency could help connection problems when several wireless devices or networks exist. I would say manually changing it for the 5GHz frequency isn’t necessary unless you have those cordless phones that use the same frequency and you experience connection issues. Otherwise not many things utilize this frequency. I suggest Automatic.

Wireless Security! or “Can’t you hear me knockin’?”
WEP (Transitional Security Network) - 13 character password compatible with WPA/WPA2 devices. Original standard (with the added “transitional” technology on the APE), not easy to remember, and has been found to be more easily compromised than WPA protection.
WPA - (option not available by itself in the APE settings) - Simple explanation: Pre-standard version of ASCII password protection for networks using 8-63 characters by default.
WPA2 - (802.11i) - Official standard for WiFi protection that uses better encryption than WPA.
WPA/WPA2 - Together at last for compatibility with older devices.
•“So what do I do?”•
If in doubt, use WPA/WPA2. If you have an old or “simple” device (Nintendo DS/DSi, cell phone, Windows pre-XP SP2) it might require a WEP password or none at all.
After seeing your APE settings, you might be asking yourself, "What the hell is 802.11a?" Well, "a" came out around the same time as "b", but unlike "b" it operated on the 5GHz frequency. At the time it was more expensive than "b", had some launch problems, wasn't really successful on the consumer side, and therefore was/is mainly used with businesses. Chances are good that you will never use it.
----------------------------------
These are the basics I feel that I see the most questions about. If people like this, I will definitely add more information (port mapping, multicast rate, guest networking, DHCP reservations and the like) as soon as I can.
Edit: This is also my first guide, so I hope it's fairly easy to understand for people, and that the information is correct for the most part. I'm still learning myself