When is it safe to socialize my puppy?

I'd do it early. The only caveat I'll give you is to make sure if you're socializing with other dogs, I strongly encourage you to do that in the right setting. I don't like taking them to places where there's a lot of other dog traffic, especially dogs that you do not know. So your big chain pet stores that let you bring pets in there—I’m not a big fan of doing that with puppies. Dog parks, groomers, boarding facilities, I will try to find any other alternative when they're puppies. When they're not fully vaccinated, I try to stay away from those kinds of activities for obvious reasons. You don't know what those dogs have or where they've been or what symptoms they may have.
Now if you have friends or family members or perhaps even have other dogs yourself, and they're healthy, and you know that, knock it out. Let them socialize. Let them be a dog.
I currently have a four month old puppy right now and I have a one year old and a seven year old dog. They are best of buds. They do everything together and that's fantastic. The little four-month-old is learning so many things from other dogs, I'm not even having to show him anything. He just follows what the others do and he's learning how to be a dog. That's okay. But of course, I know that those other two are perfectly healthy and vaccinated. In that kind of situation, do it early and often. If not, hold back, and then before you start doing trainers and other things, I would wait until they're fully vaccinated, which in most dogs is closer to, say, four months.