OK. Got the two computers hooked together through a Linksys switch/router,
and they're both online nicely through a high speed DSL modem.

Now, what are the indicators as to whether my computers are networked or

If they're aren't networked yet, but I cause them to be networked, will that
be detrimental to internet access for either?

If my computers are not networked, how do I establish a network condition
with them?