Adding a router to network in order to extend network?

Hi, I'm a happy Time Capsule owner, but due to the age of my house and its thick walls, the Time Capsule has a hard time blanketing the second floor of my house, and has spotty reception up there.

Forewarning: I'm a networking fool.

I was wondering if anyone could recommend a cheap wireless N router that doesn't necessarily need to have a great range, just enough to cover a floor.

Now, is there a way I could just have this extend the current network, and not have it as a brand new wireless network? (ie: I only want one wireless network under settings on my iPhone.)

Lastly, how in tarnation do I do this? We have a cable modem plugged into the wall on our first floor with a WLAN cord coming out of it, which plugs into the Time Capsule. We then have an ethernet cord that goes from the Time Capsule to our old PC.

How would it be possible to put a router upstairs anyway with this current situation? (WITHOUT running it all through the house and up the stairs. >_<)

I see people with houses with ethernet cords upstairs, but I just have no idea how they do it. Don't they need a central area for the modem, or are modems old, phased-out tech that we still have for some reason.