You really should read up on basic home networks before you go and screw up your parents ISP.
Goosemaster laid out the basic setup. Yes you will then have to forward ports to a internet server behind the router. To be more specific, you will have to provide more details on your equipment, and type of ISP. It would also be more helpful if your questions were not all in a single sentence. There is litterly hundreds of web pages walking you through a simple network like this. Just spend a few minutes with google and read a few. Hopefully within an hour, you will have the network you are trying to acheive.