I did that just last year. I bought this TP-Link router. Cost me less than 40 euro. I then disabled its DHCP and ran an ethernet cable from my other, main router to one of the TP-Link's LAN ports. That was it.

It's been working perfectly for more than a year now. When I'm upstairs the main router is providing the wireless signal, when I go upstairs this switches to the TP-Link. Very transparant, and it was a lot cheaper than a 'real' access point too.

Oh, and this TP-link is compatible with DD-wrt and OpenWRT too. I didn't go through the trouble of flashing the router (the original firmware works fine for me - I've never even had to reboot it), but you could do that if you wanted to.