Compiling for another machine

OK... never done this before and not really sure where to start...

I have a piece of software (iTALC in fact) and I want one of the components to run on my thin client boxes which run a HP version of Linux on Compact Flash (hence very little spare memory and no compilation tools, etc.)

The terminals use Via Eden processors but I don't think that this matters since they emulate i686 and performance isn't an issue.

I can use my laptop to compile the software and I can download source of debs off the net. How do I then go about getting said files into a format suitable for the thin clients?

Hope I haven't waffled too much ;)

There's a Cross Compiling mini how-to here:

http://linux.bytesex.org/cross-compiler.html

I don't think I need to cross compile since I will be using an i686 kernel, both are Linux (my laptop is 2.6.17 and the thin clients are 2.4.??).

Run it and see what happens then.