I come from an "eurogames" background, so in my first steps through the world of wargaming I was worried about the lengthy rulebooks, with a lot of exceptions and complicated rules.
Probably the game that helped me more in getting into wargaming was Victory at Midway, from Command Magazine #14.
I played VaM solo, but I think it's better face to face. Anyway I was very satisfied of the game, just because of the rules: they're clearly written, well organized and... entertaining too!
At the very beginning of the rulebook there is a box dedicated to new wargamers. There I found the most valuable suggestions to enjoy wargames. I will report here the most significative lines in italic: they're some kind of commandments to me.
Do not try to memorize these rules! No one does that.
Read the rules through in their entirety at least once before you punch out the playing pieces. During play, look up specific rules when you need to.
But most of all, remember - the main reason to play these games is to have fun.