For me, this is the easiest way (a cheats way too, but who gives a ...).

With C, G, F and A minor and you'll have the equipment for the vast majority of pop songs.

Throw in D minor and E minor and you're well on the way.

Start with a right hand melody and see which chord works best.

Experiment with Em and Dm, if you need a more mellow sound.

The rest is to play them until it sounds right. You'll know which ones fit together.

Once the tune sounds right, use a transpose function to make it fit the actual key of the original.

Bob's your uncle ...