Here's the problem I'm having difficulties solving:

I need to connect Computer A with Computer B via a router/ethernet. Then I need to access Computer B from Computer A and run some programs/scripts.

I'm running opensuse 10.3 on A and opensuse 11.0 on B. I was wondering how to set up this type of network. I don't need internet connection on B, just need to run programs in it from A.

With all that in mind; I would also need to add more computers to the "network" after. All of which with access to each other.

Thanks for everyone's help in advance.

You don't need a router. If you only need the machines to talk to each other, you only need s switch or hub. I recommend a switch because they're not that expensive these days and they'll provide better performance. You technically don't even need the swtich for just two computers, but you mentioned adding more later.

You'll need to assign ip addresses somehow. With only two computers, you could just assign them manually. Pick a subnet in one of the rfc1918 subnets. (http://www.ietf.org/rfc/rfc1918.txt?number=1918) and just configure a different ip address for each machine. If you expect your network to grow large you may consider setting up a dhcp and dns server to automatically assign ip addresses and map hostnames to them.