Can a PS3 connect to a........?

May be...

I was wondering if a PS3 can connect to a TDS or CenturyTel router?

As long as they broadcast wireless G. Make of router is unimportant.

yes, ps3 can connect to any router, either wirelessly (if its a wireless router) or via ethernet cable

As long as you have a wireless router and network set up it should connect...