A bomb
Bombs can be found at airport (little icon on the map). When you 'collect' it, you are going to get a star for robbery (4 minutes, 2 minutes jail time.)
Final Step: Blowing Up the Vault Door
This is pretty straightforward. Just interact with the door, select "Plant bomb", take a step back, boom! Now you have 10 000 dollars!
Gun and some ammo
Again, easiest way to get this is getting the police job. You get Glock and about 50 ammo + cuffs + taser. Of course, you are gonna need some money to get the job, but assuming you just joined and didn't die, you have 1000 dollars.
Head to the Bank
The bank is near gas station, after the bridge. Look at the map and look for it's icon. If you are on popular server, I'd suggest you to leave your car behind the building or somewhere where people don't notice it and steal it or wait for you to come out and shoot you.
Inside the Bank
There are 3 cops, 2 on the first floor and 1 down next to the vault door. If you have no stars and you have cuffs, you should arrest the cops. This usually is the best option, because they won't respawn and kill you after you are done.
If you don't have cuffs, you can shoot the cops. But be careful, if you kill them, they are going to respawn in 10-20 seconds. If you get lucky and/or your aim is good, just shoot them until they drop, but won't die.
3rd and final cop downstairs shouldn't be a problem, unless you are slow or you have bad aim.