Maintenance for the week of September 30:
• [COMPLETE] Xbox: NA and EU megaservers for patch maintenance – October 2, 6:00AM EDT (10:00 UTC) - 12:00PM EDT (16:00 UTC)
• [COMPLETE] PlayStation®: NA and EU megaservers for patch maintenance – October 2, 6:00AM EDT (10:00 UTC) - 12:00PM EDT (16:00 UTC)
Go into launcher settings (circle icon in top right corner) and choose your megaserver. Keep in mind that items bought in the crown store on EU won't be available on NA and vice versa.
Also you should know that you'll need to download the entire game a second time for the second region, this game isn't like WOW or Rift where one client works for both regions.
Oh...will I need an entirely new account to log into it as well?
No, not at all, it's simply how the game client is packaged that means you need a separate install.
When you run the Launcher you select which region you want to play, that determines which game client (ESO.EXE) is run, your single account is valid for both.