The thing with Mafia is that explaining it is the hard part, but playing it is pretty simple. After the 2nd game the gist of it was incredibly simple. Just talk and discuss who's most suspicious and worthy of getting voted off and hung, hopefully survive the Night and use an ability if you've got one, then start Day 2 with more information to work with.
The moving gears in basic Mafia are very simple. What makes it complicated is that it's a people's game, and you and your personality has to mix and mingle with everyone else's. Are you observant, quiet, and analytical? Are you aggressive, straightforward, and willing to make bluffs in order to catch Scum? Or are you more subtle, clever, and devious? The mixing and clashing of the various personalities in these games is what makes Mafia so infinitely interesting, complicated, and enjoyable. The people make Mafia complex and engaging.
Currently we're playing a Mafia game that's classified as an Open Setup. What this means is that everyone will know the pieces being used in the game, and the factions as well, including the number of their members. It's made so that nothing is unclear, or hidden by the "fog of war," where you have absolutely no knowledge of what may or may not be in the game outside of your special Role PM (Role PMs are where I give each member their role in this game, their win condition, and any abilities they may have).
Also, the current game and the next will be normal, Classic Mafia. It is for newbies, and very user-friendly. If you're really interested in playing Mafia, Game #5 would be the perfect opportunity. Also, if you'd like to get your feet wet but you're having time constraints, I can always give you more leeway to play, for your convenience.
Consider all of the character traits that make people human. Mafia utilizes most of them, from patience and curiosity, to pressure and deviousness. Chances are your ability to discern lies and your ability to tell lies will improve, too.
Like in political debate, you use your wits to cleverly pick apart the arguments and posts of other players, trying to sift through them in order to tell if they're lying or not. And, unlike political debate, you can get people lynched at the gallows!

[MENTION=27143]BluesMistress[/MENTION]
[MENTION=44368]Chuckt[/MENTION]
[MENTION=39852]TheOldSchool[/MENTION]
[MENTION=47390]DriftingSand[/MENTION]