You will most like need a router instead of a switch in order to get both online.
A
router can share a single public (or WAN) IP between several computers, a switch can't.
But I will need to know more about your internet connection in order to be sure.
What type of internet connection is it? (A)DSL, Cable, Satellite, etc.
What networking equipment do you currently have set up? I'm guessing a modem and a switch.
Can you tell me the brand name and model number of the modem and switch?
You might want to call your ISP and ask them how many IPs are included in your current subscription.