As others have mentioned, most consumer-grade routers do not have Wireless Repeater capability in their firmware. If you have a router supported by one of the Open Source firmwares (such as DD-WRT, OpenWRT, or Tomato), then you may be able use them instead. DD-WRT maintains a database of hardware it supports on its website, although the original router most of this work stems from is the venerable Linksys WRT54G (prior to hardware rev-4).
Once you have the firmware flashed, it is relatively easy to get it into Repeater Bridge mode. Here is a HOW-TO from the DD-WRT wiki.
I have pretty much this exact setup configured at home with a pair of WRT54GL routers (~$50 each at pretty much any place that sells commodity hardware, both computer stores like Tiger Direct as well as places like Best Buy). The only thing to watch for is a little extra latency if you're on the repeater and sometimes the two can briefly lose sync. It works just fine with WPA security on both routers. I'd also suggest using a different SSID for the Repeater so you can easily keep track of which your devices are connecting to (as opposed to letting the device firmware roam between them... sometimes you get stuck on the far router which results in a pretty choppy signal until it decides to roam back)