They're currently down, but if you look at your Character Page, there's a tab up by Equipment and Settings that says Battles. The dev team might have a few test battles coming up that you can participate in to get a feel for it and help them out in the process too. They're gonna need a week or two to polish the game and work out some bugs, but it'll be back before you know it.
Would be a good time to set your character as your main, and change his timezone in Settings on the character page though, because when I first started trying to play battles, the times were 7 hours off and it confused the hell out of me, haha