What do i need to do to get my new computer connected to the internet?

how difficult is it to hook up my new computer to the internet? my current unit(dell2400) needed a disk from my isp to connect.will a disk be needed to get my new computer(sony vaio js all in one pc) onto the internet? i have DSL from fairpoint( my phone company) and a westell 2200 dsl modem as well as a belkin wireless router for our laptop.I'm hoping it's nothing more than taking the modem cord from my current unit and plugging it into the new computer.I am extremely computer illiterate.thank you for any help you can provide.