You have to get a ship called a Caravel (or at least I think that's it). When you have that the radar map at the bottom left will have a black strip to represent uknown land. Sail into it with the Caravel and you'll get to the New World. It takes a while to sail though, so make sure you put a huge army on the boat, not enough time to keep going back and forth. Im not sure if you have to wait a certain time before you can build a caravel or if its available as soon as you get the appropriate port. Either way you'll get it eventually, just keep upgrading one of your cities.

and Welcome to the forums.