The core vaccines are DATPP, distemper, adenovirus, parvo, and parainfluenza, and rabies. There are some other non-core vaccines that we recommend later on.

From day one, your puppy should absolutely receive what's called DATPP. That's distemper, adenovirus, parainfluenza, and parvovirus. And from then, every three weeks, they'll receive that same vaccine, plus some later on.

Well, most vaccinations for puppies come in a combination, and the big ones that most people are familiar with and are probably still the most important are distemper virus and parvovirus. That doesn't mean that those are the only two that your dog needs because there are other things like coronavirus, not the same one, a different canine coronavirus, hepatitis, leptospirosis. Those are all things that can be included as well. But distemper and parvo are probably the two most common that we still do see from time to time in practice on young, unvaccinated puppies. So, I think those are the most important ones.

Just exposure early and often is the best way. I don't have a formula. Every dog is different. But it's just exposure. Start with a leash so you have them under control. You don't know how those other animals are going to react. So do it in a controlled setting where they're both leashed, but start small. 
If one or both of the dogs are either acting aggressively or perhaps the other way, being very fearful, do it very matter of factly. Just take them for a walk and let them get close to each other, but keep on walking. And then as they get comfortable and they realize it's no big deal, maybe then you make another pass and they get a little closer. Or maybe you stop and talk with the owner. Try to mimic a normal day-to-day situation that you might run into.
Start early. Do it often. If you can implement any of this, trust me, you will be happier for it, and you're going to have a much better, well-rounded dog when it comes right down to it.

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.