Worried about networking with new comp.

Hi, I bought a new computer today. Waiting for it to make it to my house. Rather than going wireless, I went with the 56K PCI Data Fax Modem. Now I still will be using another computer which is currently hooked up to the cable modem and router. Now my problem is I want my new computer to just hook up to the router for the internet. Can I just plug a Ethernet cable to my new computer and router and go? Reason I ask is I no longer have my router cd. I tried doing it with my laptop and I got internet but I'm just worried it wont work with a desktop. Any help will be appreciated and if anything needs clarification just ask.

 

yeah just plug it in, it should work.