A great strategy for playing a game you should never play!
Step 1: Never Play Russian Roulette!
It's dangerous and you could die.
Step 2: If You're Being Forced to Play Russian Roulette by Some Psychopath,
this guide is for you.
Step 3: Familiarize Yourself With the Particular Revolver You'll Be Using.
Some cylinders (e.g. the Colt Police Positive) rotate clockwise from the rear. Other cylinders (e.g. the Smith & Wesson Model 28) rotate counter-clockwise from the rear. This is super important!
If your cylinder rotates clockwise from the rear (e.g. the Colt), the chamber just left of the one aligned with the barrel (when the hammer is down) is the one that's "up next". If your cylinder rotates counter-clockwise (e.g. the Smith), the chamber that's up next is the one just to the right of the one aligned with the barrel. For sanity's sake, this is all from the perspective of looking at the revolver from the rear, i.e. when holding it while aiming away from you.
If the gun is already cocked, or the trigger is already mostly pulled, the cylinder has already rotated. The chamber that will fire is now the one already aligned with the barrel.
Step 4: Learn to Spot Whether the Gun Will Fire or Not With the Next Trigger Pull.
This is based on your ability to see, feel, or otherwise determine whether the chamber that is "up next" is loaded or not. This will be the chamber directly left or right of the one aligned with the barrel, depending on which way the cylinder rotates on your particular revolver.
Usually, it is possible to see a little sliver of metal corresponding to the rim of the cartridge from the rear of the chamber. On some guns, you can even see it from the side.
In this photo of a Smith & Wesson Model 28 in .45 LC, the gun is ready to fire. You can tell because the chamber just to the right of the barrel is loaded (see the little silver sliver?). Because the cylinder rotates counter-clockwise from the rear (on this particular gun), we know that the loaded chamber is up next.
Get familiar enough with this concept that you could trust your life to it if you had to, but don't gamble your life on it unless absolutely necessary. Remember: in Russian roulette, there's no prize for second place.
Step 5: Enough Talk. Time for Action!
The psycho who is making you play RR will kill you if you try anything funny, so play along.
If the chamber that's up next is empty, you can pull the trigger on the revolver, and nothing will happen. You will hear a "click", and it will advance to the next chamber.
If the chamber that's up next is loaded, shoot the psycho, save the girl and escape the palace before it blows up.
Step 6: Caveat...
There's probably more than one caveat involved with playing RR, but this is one to beware of.
When you initially close the cylinder on the revolver after spinning it, there's a good chance it won't align perfectly with the locking plunger that fixes it in place. The gun will essentially be "between chambers", and it will be difficult to reliably determine which chamber is up next.
The thing to do is, immediately after closing the cylinder, rotate it slightly with your fingers (either direction) until it clicks into place. Now you can check the chamber that's up next to see if it's loaded or not. Prior to clicking the cylinder into place, it's anyone's guess which chamber is up next.
Step 7: Enjoy!
Be safe, have fun, and as stated, never play Russian roulette... unless you're forced to, in which case, remember what I taught you, and good luck! :D