Solo / Silent bank job in Payday 2, no civilian casualties.
The first order of business when taking on a bank silently is to eliminate the guy in the security office. This can be done either by taking the keycard from the wandering bank manager (the guy in the vest), or by using an ECM Jammer, if you have the appropriate skill. It's all about patience - if you wait by the stairs / back door, he'll eventually wander through, either to go to the roof or to go out back for a bit. Detain him there, and take his card.
Once you've eliminated the guy in the security room, the cameras will be effectively offline (though you can still use them to find the guards). From there, you want to systematically eliminate the guards. The safest way to do this is to wait until they walk into the back hallway (again, either to go outside or up to the roof), and take them out there. If the security room is located on the other side of the bank, you can hide the bodies in the dumpster out back, or on the roof.
Once the guards are down, you'll need to detain any civilians in the general vicinity of the vault. If your vault is where mine was, this is easy to do. If your vault is in front, you'll probably want to use a silenced weapon to kill the two bank tellers, because the majority of the time, they'll immediately press the alarm button if you try and detain them. Additionally, there's usually many more than 5 civilians in that area, so you'll need to either kill the extras, or stand there and yell at them constantly.
Once you've got the area under control, you can drill and loot the vault like normal. There's nothing stopping you from taking all of the safe deposit box loot; I didn't here, in interest of time. If you've got a Cash or Gold bank heist, you'll want to make sure the streets are clear before you start ferrying the bags to the van - you can detain people on the streets, but be careful nobody else sees you do it.
As you can see, the drill doesn't make nearly as much noise as it seems like it does - I'm not using any of the sound-lessening perks in this demonstration.
Required Skills: None
Recommended Skills: ECM Overdrive (This will let you open the security office without needing to find the keycard)
Cleaner (Ace) - This makes eliminating the guards a lot easier, as you can stash the bodies somewhere safe.
Dead Presidents (Ace) - If you're planning to clean out the safe deposit boxes, this will give you a pretty great cash boost.
Smooth Talker - Most banks have at least 3, sometimes 4 guards, and this will let you take all of them out with ease.
Dominator - If you don't have Smooth Talker, Dominator will help you eliminate the guards. If you do have Smooth Talker, sometimes it's easier to detain them than worry about the pager.
Cable Guy (Ace) - You'll almost always need more than two cable ties to detain all of the civilians. Without this, you'll have to kill them.