Battlegrounds have brackets. There are 5 brackets (I think) that are labeled as 10-19, 20-29, 30-39, 40-49, 50-60. Those are the levels you can go into each one. So if you go to a battleground master and want to sign up it will put you in the bracket that your level consists with. The battlegrounds are in every major city (Undercity, Orgrimmar, Thunder Bluff - Horde - Stormwind, Darnassus, Ironforge - Alliance) and at their respective zones. The current battlegrounds are Warsong Gulch (WSG), Arathi Basin (AB), and Alterac Valley (AV). You can enter WSG through each bracket, AB after level 20, and AV after level 51. You can enter the BG's at their respective places in the world also. WSG in Ashenvale, AB in Arathi Highlands, and AV in Alterac Mountains.
You can start at level 10. Most people frown on this because you will get killed by just about everyone on the opposing team. I would suggest level 15+ because you can hold your own and if you know your class you can do pretty well. Starting early will allow you to get used to it and can get you an outlook on what your going against in world PVP.