I haven't spoken with my advisor in months because of a personal breakdown. How do I reestablish contact?

It should be enough to explain your absence with "I've been ill for several months, but am better now". You don't really need to go in to details. If asked, just reply that it is very "personal".

The professor may need some assurance that you will be effective going forward, but really has no need to know details.

And, of course, you should say you've been somewhat (at least) productive in the interim.

And keep contact with the professional counselor through any necessary transition.

I'd also go through some channels at your university that offer support to students going through difficult times in their lives. Having referred yourself to them will lend you some support in case things get hairy, because it will (partially) legitimise your lack of communication. That said, I disagree with Buffy, in that you shouldn't hide the issue so much from this professor. We're all human at the end of the day, and it would be a welcome approach to just be a little more candid with what you've gone through. This doesn't mean you have to reveal every detail, far from it in fact, but don't just say that you had "personal issues". That sounds like a copout and may make you look like someone who's just finding easy excuses for their lack of progress. Finally, I'm sure that them seeing you being able to overcome your issues and be ready to get to work again will display you in a positive light, as it will highlight your determination and desire to continue your work. I've seen people quit PhD's over far less.

You're a trooper, stay strong, chin up. There's always a light at the end of the tunnel. As someone who has suffered from depression for numerous reasons (partially down to parental issues as well), I can only empathise but at the same time remind you that no matter how hopeless the situation may feel, it's never the end of the world. :)