Forgive me for being skeptical, but let me give you some tips anyway, just to make sure you’re on the right page. I’ll start from the beginning (I’m not trying to be patronizing, if I come across as such, I apologize in advance), but I promise to make it worth your time.
Right away, when you look at your cards, you should note two things: (1) how high your cards are, (2) whether they’re paired or suited. The very best hands are both high cards and either paired or suited. Of course, the best hands are high (A-J) and paired/suited. Very few people have problems telling what the very best hand to start with is: AA.
If you stick to playing only the very best hands, you’ll basically play only those, end up sitting around 95% of the time, get bored, and piss off your friends because you stretch the game out.
So, basically, which hands are “good” depends VERY VERY VERY much on your individual situation. If you’re playing with friends, you’re entitled to play more hands than you might otherwise. If you’re playing for fun, you’ll want to play more hands than if you’re playing to make money. If you’re on the button, you have good position (you get to see everyone else act before you have to commit), and you can play more hands than if you’re in early position.
For certain hands (high pairs), you’re in a good position to start off, in the sense that you have a high probability of winning, and a low probability of splitting the pot. For other hands (suited connectors and low pairs), you’re in a bad position to start off – but you have a slim chance of getting lucky, and although you’ll be losing 90% of the time when you play them, when you do win, you’ll win big, so overall you come out positive.
When you’re in early position (under the gun, for instance), you want to stick to the best hands and leave out the speculative hands. When you’re in late position (on the button, for instance), you have the freedom to play more hands.
A good book to read is Dan Harrington’s book on No-Limit Poker. It’s expensive, but will likely pay for itself in the long run.
Well, the easiest way to tell when it’s your turn is when people turn and look at you. 
The second easiest is to go when the person to your right goes. 
(that is, unless you’re the small blind)
The easiest way to keep track of the bets is to remember them as multiples of the big blind. For example, if you’re playing 10-20, then the big blind is 10, but count it as one bet. The minimum for betting is one “bet” before and after the flop, and two “bets” after the turn and river.
The minimum for raising is one multiple of the last bet or raise. So for example, if someone bets 10, you have to raise at least 10. If someone bets 10 and someone else raises to 50, then you have to raise in multiples of 40. Keep in mind that sometimes people like to raise “to” a certain amount (i.e. bet 10, raise to 100 = bet 10, raise 90), while some people like to raise a certain amount (i.e. bet 10, raise 10 = bet 10, raise to 20).
As for knowing how much it is “to” you, there’s no easy way to tell. It’s the current bet minus what you’ve already put in. You bet 10, someone raises to 20, someone re-raises 60 more, and there’s no easy way around the math – (20-10)+60 = 70 to you.
With a little organization, you can make the process a little easier: don’t let people “splash” the pot (throw their chips haphazardly), and force everyone to keep their bets in nice piles in front of them. When the betting is done, collect all the chips into the middle, freeing up space for the next round of betting. This way, it’s easy for everyone to see what was bet this round (as opposed to what was bet last round).
Next time you watch TV, note how the dealer will sweep everything into the muck, giving players space (and also to prevent cheating!), and players will be nice and stack their bets into appropriately-sized stacks (i.e. if they bet $1000, they will put out 10 $100 chips stacked in two stacks of five).
I also appreciate the book recommendations, but there’s no way in hell I’m going to read about poker. It’s just not something I’ll ever take that seriously, plus I’ve always been one to prefer learning by doing: I’ll figure out what I need to know by simply playing.