All of the descriptions that follow are for a right handed thrower throwing backhand. For a lefthanded throw, reverse everything. For a forehand throw, reverse everything. Which means that a left handed forehand throw will behave like a right handed backhand throw.
Flying discs differ in their flight characteristics. There are three general types of discs, overstable, stable, and understable.
The heavier a disc is, the more overstable in tends to be. The lighter it is, the more understable it tends to be. Also, as a disc ages it will tend to become more understable.
Given these different characteristics, you will sometimes have to vary your angle of release in order to get the disc to end up where you want it.
So let's say you're right handed and have a very overstable disc. You want it to end up straight ahead of you so you throw with anhyzer. Your disc starts out flying to the right but soon flattens out and comes back left.
Similarly, if you have an understable disc and you want it to end up straight ahead of you, you should throw it with hyzer. It will start by flying to the left before flattening out and flying to the right.
One important thing to keep in mind is that, given enough time, a disc spinning clockwise (right handed backhand or lefthanded forehand) will eventually fall to the left (and a disc spinning counter-clockwise will eventually fall to the right). Many times a thrower who wants their disc to turn right will get the nose up on it and it will hyzer out, meaning it will fall back to the left. This type of throw is generally followed by muted (or maybe not so muted) cursing and the occasional kick to their bag.
Ok, so now you've got your stables and your hyzers all set and you're on the tee pad staring into the teeth of a fifty mile per hour wind. You have a nagging feeling that your disc won't fly quite like you've been told. You are absolutely right.
A headwind (wind blowing in your face) will do several things to a disc in flight.
So with the wind blowing in your face you might want to throw a more overstable disc to keep it from turning over, or you might want to throw with hyzer so when your disc does turn over it will go from left to straight instead of straight to right. Of course, if you're playing in a hurricane you'll want to do both.
A tail wind (wind blowing from your back) will also do several things to a disc in flight.
So there's a huge tail wind and you want to take advantage of it, you throw an understable disc and get it up in the wind a little bit. Because it's understable it will take longer to hyzer out and in the meantime you get to see your beautiful little disc fly hundreds of feet towards (presumably) a basket.
If you're just starting out and unsure of what (or how) to throw, there are a few quick guidelines that will help. The first (and, to me, most important) is, throw light discs. Yeah, the pro at your course is throwing a 180g viper 500 feet, but forget about it. Start light, you'll get better arm speed and better distance, as well as putting less strain on your body. Once you've gotten comfortable with your throw and your light discs are starting to turn over, then start to experiment with heavier weights. In general a light disc will fly just as far as a heavier one. The world distance records for women and masters were set with 150g or lighter discs and the overall world distance record was set with a 169g disc. That said, if you can generate the same arm speed with a heavier disc, it will go farther because it has more momentum. Also, most players are more accurate with a heavier disc.
The second guideline is to start with a stable or an understable disc. I'm a huge fan of the stratus, stingray, comet, and shark as beginner discs. Lightning also makes some extremely user-friendly discs that are good for beginners.
Third (once you have your light, understable disc) is to keep your body relaxed through your throwing motion. You should concentrate on releasing cleanly and keeping the nose of the disc down. If you get the nose up your disc will stall out and fall off to the left, costing you distance and accuracy. You can generate lots of arm speed (and, thus, distance) by reaching your throwing arm back across your body as far as you can and pulling the disc straight through (as opposed to around). Finally, you can get a good "snap" on the disc by holding it tightly (but not so tightly that the rest of your body tightens up).
John Houck has a video called Learn to Play Disc Golf which does a good job of covering the basics and Scott Stokely has come out with an instructional video series which is probably the single best resource available for learning to throw. There are also articles in many issues of Disc Golf World News with suggestions to improve your throwing technique. Probably the best source of information, though, are the good players around your home course. Watch them and talk to them, ask if you can play a round with them, most of the time they will say yes.