Assuming you have a 3 piece crankset, don't need to repack the bearings with grease, or you don't have a sealed bottom bracket, you may be able to do it without a crank puller.
You will need a 36mm headset wrench.
The right side (when you are riding the bike) is called the fixed cup- there should be 2 flats for the 36mm wrench to fit on. If your bike is NOT french, it tightens COUNTERCLOCKWISE. Tighten that up as much as you can- putting all your weight on it.

If it is still too loose, then you'll need to fiddle with the adjustable cup on the left side of the bottom bracket. You will need a lockring hook wrench (or a pair of channel locks for ghetto style) for the lockring and either a pin spanner or a 16mm open ended wrench for the adjustable cup.

This side of the bottom bracket is conventionally threaded so clockwise tightens, counterclockwise loosens, like any regular nut and bolt. Loosen the lockring a few turns.

Tighten the adjustable cup just until the play in the BB spindle is gone.

This is where the tricky part comes in: holding the adjustable cup in place with the spanner or wrench, tighten the lockring with the hook wrench or channel locks as much as you can.
If that doesn't fix the problem or you don't have the right tools, it's time to bring it to a shop or to one of yuor know it all friends who can take care of it for you. There's a lot of practice and experience at hand to make this a quick and successful operation. and about $100 of tools.