1) It's best to ask for a second date at the end of the first one, but yes, you should call her and ask for a second date. If she doesn't answer or doesn't call you back, it's a no.
2) Go somewhere different than the first date. You make the plans for the second date, don't go into it not having a clear plan; decide on two places to eat, call them "place a" and "place b", make sure they serve different styles of cuisine.
3) Never plan on making it back to the girls house, that way you'll never be disappointed. Having you over means she wants you to make a move (this is where the "DVD and pizza" date's reputation comes from). Instead plan some activity where you'll have time to talk while doing something (bowling, hike, etc.)
4) Leave the guitar at home, to me it comes off lame for a second date.
Keep your love life off Facebook, don't cheat, it's never too soon to make a move on a woman you like.