Now that we went over communication, let's have a look at gameplay basics. Step 1 might simply be to select what difficulty level you're going to be playing at. If you just bought your first rifle at level 5, chances are you're not going to be very valuable yet in any Overkill heist, let alone a Pro Job. Leave those be for now. In fact, you'll usually want to have played the heist a few times at Hard or Very Hard before you dive into Overkill. There's a pretty big gap in combat difficulty there, so knowing the maps shouldn't have to be an extra issue.
When it comes to map specifics, there's actually quite a bit to learn in Payday 2. From knowing the way to pick the right engine on Big Oil, to understanding that on Watchdogs Day 1, the car will arrive after you throw in the first 4 bags - and thus, you should get all bags ready to throw first. Of course, these things by themselves won't often be reason for a kick, but it adds up. All in all, it really pays to get the maps down on the lower dificulties - games are a lot more forgiving there. But understand that if you ran out of the bank with a bag of gold and barely made it to the van, you probably won't make that same distance on Overkill. On a small side note; Normal Jewelry Store is a bit of an exception here. Speedrunning is a common way to grind for cards, and if you lag behind, you'll get escorted out before the 1 minute mark.
Now let's say you understand how to do these Bank Heists by now - you join an Overkill lobby, and notice everyone else is in suits and has ECMs equipped. It's a dead giveaway that it's a stealth run, and if you're not familiar with that, that's usually fine. Most people I know don't mind a non-stealth player sitting in on their stealth runs - but try to stay out of the way. If you're following around someone sneaking past a guard, while you're wearing 75 Visibility gear.. chances are it's not gonna be appreciated. Try to observe (and ask) rather then jump in if you don't know what's going on. As an example, I'll often run ECM rushes on Firestarter Day 2 with people unfamiliar to the concept. As long as you either stick to the spawn, or go directly for the evidence room and don't shoot anyone, you're working towards the team goal despite not being familiar with the strategy.
Lastly - and this is a major point for a lot of hosts - try to be a team player. If your buddy runs past a Shield and the Shield turns - pop that sucker! Drill broken and you're close to it - fix it (this is something even experienced players have trouble doing, sometimes ;))! Not sure what the hell to do? Ask. If there's nothing particular to do but fight off cops, do that. Make sure to watch your armor and ammo levels, stay within reasonable distance of your teammates, and mark any special opponents!