Hi,
Just got the game and have no idea how to fight. I equipped a bb gun with the tab key but I have no idea how to use the thing. I ran into this little bug thingies, tried pressing V for the VATS system but nothing happened, clicked the mouse a million times, wtf is going on? How do I work this game?

R is the default for Reload/Ready/Unready a weapon.
Unready is R pressed and held.

Left Click is usually ready or fire weapon.

A gun is useless if it has no ammo, usually.
Melee weapons are your backup for when you run out of bullets.
10 mm Pistol may do more damage than the bb gun btw, if you have ammo.

"When all else fails, read the manual" - Old saying
Check over the one you got when you bought the game.

Yes, press R to make sure you're pointing your weapon. (Pressing R again will put your weapon away.)
Then make sure you have BB gun bullets, if you're using the BB gun. If you don't you may need to go back into the vault to look for some.
Left-clicking on the mouse shoots the weapon.
If your weapon isn't pointing (if you can't see your hand holding it), then VATS and shooting won't work.
If you have no weapon with bullets, you can use your hands or another melee weapon (a baseball bat or whatever other weapons you find lying around). To do this,
you'll also need to make sure that you press R so that your hands come up in front of you, or the bat, or whatever, then you click the mouse (left).