I've doing a few fantasy drafts and I've noticed a few things.
1. The wingers go fast. If you need to get your wingers, take them before your centers. Many leagues are designed where you need two times as many wingers as you do centers. The fact of the matter is that the majority of scoring forwards play at center (so theyre in the slot), and the wingers are left with much less depth. However, if the franchise wingers go first, you will need to prioritize a bit.
2. Take your goalie in the second round. Unless its Luongo, get your hands on a franchise forward first. The exception is if there is only one franchise goaltender left, whereas there are a few solid forward picks left. If that is the case, lock up the goalie, then have a few options left for a good forward.
3. Watch what other players are lacking, and will be looking for. The casual player doesn't scrutinize what other people are doing. In other words, if everyone after you has their goalies, don't take a goalie. If you need that goalie badly, wait for the next round when it's your turn again.
4. If you're at the end/beginning of rounds, take two different types of players. You want to diversify the picks you make so to get your hands on the players you need in every category. Stocking up on only forwards or defense at a given moment will cause you to have less depth the next round, and you will likely make a 'desperation pick' as I call it. A 'desperation pick' is when you take a player based 100% on his playing position and not on his merit. For example, if you grabbed Fredrik Norrena because you needed a goalie badly when Mats Sundin (or someone in the 70 pt range) was still available.