you would need to configure the computer with wirelesss as a router, to do this you need to get bind (
http://www.isc.org/), and iptables (
http://www.netfilter.org/), bind is the dns server, ipfilters configures your routing and firewall, if you want to go it alone download those and read there man pages, but since that will not be enough (there is to much to figure out on your own in a reasonable ammount of time) I recommend this tutorial:
http://www.tldp.org/HOWTO/IP-Masquer...WTO/index.html but it is VERY long and has more information than you need, and it does not cover dns, if you want the quick and dirty snag this script it lists:
http://www.tldp.org/HOWTO/IP-Masquer...FIREWALL-2.4.X and make whatever changes you need for your network cards (eth0 eth1, etc.)
then you will need dns, the above will let you ping and browse sites by ip address, but to resolve the domain names (
www.google.com for instance) you need the dns working also (both dns and iptables should run on the machine w/ the internet connection)
here is a good dns howto:
http://www.tldp.org/HOWTO/DNS-HOWTO.html I recommend you read this, it is not to long and will give you lots of valuable information about how networks work and how the internet woks, you will not be disappointed, but if you just want the quick and dirty (requires skimming still in other sections):
http://www.tldp.org/HOWTO/DNS-HOWTO-5.html you need to read everything up till this, and then this, after it is just fine tuning and advanced settings.
this may seem overwhelming at first, but do not let it scare you off, and do not give up, 4 months into my linux usage I got 2 servers liek this up and running (sharing 2 56k connections) (5 years ago) and I even including dhcp (automatic IP address assignment)
oh, and after the router is configured you need to issue this command on the other box:
route add default gw 10.1.9.1 eth0 netmask 255.255.255.0
this will set the server (10.1.9.1) as your default router to connect to the internet, gw stands for gateway(router) I recommend reading the man pages and help for the route command it is confusing as hell and almost prevented me from succeeding