A question about my new computer and connecting to my ISP?

I am replacing my current computer with a new Vaio js series all in one desktop that is equipt with wifi.i already have a belkin g series wireless router that i use for my laptop,as well as the dsl router for my desktop.my question is,what do i need to do with my new computer in order to acess my current isp and the internet? I am seriously computer illiterate,i'm uming all i need to do is either plug in the ethernet cable and be ready to go,or just set the sony to pick up the wireless signal from my router.I'm hoping that it's simple.can anyone please help me? thank you.