IP Address issues & mapping other drives

This is a request for help. I hope I'm on the right track.
I've got a wired Linksys router, 2 computers running XP and 1 running 2000 Pro. Usually I need to use ip addresses in order to map drives. I don't know if I can set up a DNS server or how (or even if that would help). The problem is, of course, when the computers are turned off, or I have to boot the router, the ip addresses get switched around (3 different addresses are assigned to these "named" computers, at random). Is there some way to either assign these LAN ip's permanently, or is there some way to set up one computer as a DNS to acheive this??? The host files help until the ip addys change again. One machine (mine) tends to stay on all the time.
Any help will be greatly appreciated.
Steve

Ok, and thanks. This brings up my second stupid question. I remember at one time accessing a "web page" which controlled my router. This faint memory is being held by my last 2 available brain cells. Was it an IP address entered in IE?? How do I change Router settings?

Thanks so much. This jogged my memory. It turns out it can't be done with MSN Explorer (which I actually like). Using IE it took me right to setup. Everything looked OK, so I went to Linksys and downloaded their firmware update for this Version 2 (of 4) router. I was running Ver 1.42.7 dated 4/2002. I updated to 1.46.2 8/2004 !! From the readme file...
"1.46 June 24, 2004 1. Fixed DHCP renewal."
I set the lease time to ~34000 and updated and copied HOSTS to all the machines. No more need for ip addys and everything is running very snappy. Thanks for helping with this long term pain in my neck. !