First, is everything through it slow? That is, is a hardwired Ethernet connection just as slow as wireless? If not, that narrows it down to the wireless end of things. If so the problem is either the base station, too much traffic, or a modem issue.
If everything is slow, how about bypassing the airport and connecting something directly to the modem. If that's fine, then you've further narrowed it down. If it's also slow, it's either your household wiring, the modem is flaky, or you have an ISP problem--call them in any case.
If that's fine, then try turning off everything but one computer. If it's fine then, it's being slowed down by either one of the computers doing something weird or some software on one of them (most likely file sharing, though if you have PCs it could be a virus or other malware as well). If one is fine add the other machines back one at a time and see when the problem returns. If one isn't fine, try a different one alone just to confirm.
If none of that pins it down, have you checked if there's someone else hijacking your wireless network to do a bunch of large downloading? You should be able to see what all is connected in the Airport utility, and you'd also see the activity light on the airport and modem flash even if all your computers are asleep or turned off.
If none of that helps, try a full reset of the Airport, and update its firmware if it's not up to date while you're at it. You'll have to re-enter your settings but this will get you back to a clean slate. If it's STILL not ok, then a hardware problem is all that's left, and time to either go warranty or buy/borrow a replacement to confirm that a new one works properly.
