Enable IP forwarding as directed in wolluf's second link.
While your changing things, keep in mind that routing takes place between networks, not between hosts. Using enkie's diagram and using a 255.255.255.0 subnet mask everywhere, you would give computer 2 an address of 192.168.2.12 and the NIC in computer 1 that is connected to computer 2 an address of 192.168.2.11. Computer 3 would get 192.168.3.13 and the NIC in computer 1 that is connected to computer 3 would get 192.168.3.11.
I would skip the 192.168.xxx.1 addresses, as many broadband routers and switches like to use those addresses by default, so avoiding them now could save you some work should you add such a device later.
Once the addresses are in place and you have enabled forwarding on computer 1 (only computer 1 needs it), add a route on computer 2 ('ROUTE ADD 192.168.3.0 MASK 255.255.255.0 192.168.2.11 /P') and computer 3 ('ROUTE ADD 192.168.2.0 MASK 255.255.255.0 192.168.3.11 /P'). The /P makes it persistent so you don't have to add it after each restart.
At this point you should be able to ping all of the computers. Browsing will not work. As bcastner stated, the broadcasts needed for name resolution are not routeable, so they will not make their way from computer 2 to computer 3 or from computer 3 to computer 2. A lmhosts file on each machine should fix that up, also as mentioned by bcastner.