The best method would be to play a Super-Hero RPG similar to any RPG you players currently like. If you are completely unfamilar with RPGs, I would suggest either edition of the Marvel game or the cut-down introduction to DC Heroes (the Batman game).

If your players are familar with D&D, then choose either Villians & Vigilantes (if you can find a copy) or Palladium's Heroes Unlimited. If any of your players have liked Rifts, then Heroes Unlimited is the optimum game.

If you can handle the slightly slower pace, but heavily detailed and long playtested rules appeal, consider real Champions (aka The Hero System). The combat rules are excessive for some players tastes, and character creation can prove very time consuming to create exactly the desired character. (If you can keep from using every option and permit the players not to balance out the characters fully at first, Champions plays much better. Expect your players to redesign characters multiple times.)

Do not however be deceived by fake Champions (aka Fuzion). The rules assume a knowledge of both Champions and Interlock, the ancestor game systems. While the rulebook takes fewer pages, this was accomplished by throwing out most of the descriptive and explanatory text and by making the text so small that a magnifying glass will prove most useful.

The support product I would recommend you look at the most is Gold Rush Games San Angelo, a well detailed city designed to generate subplots. If GRG is still offering the San Angelo and Champions 4th edition bundle, I would suggest you definitely consider picking them up.