Depends on how much time/effort you want to put into it. First check out ESPN.com, NFL.com, and Fantasysports.Yahoo.com for their fantasy football stuff. Then you can check out the following:
1) Know your scoring rules. 4pts vs 6 pts per passing TD changes the QB values a bit. Points for receptions or performance (extra for 100 yard games, etc) can make some players more desirable in the long run.
2) Create a cheat sheet. List the top 100 and say the top 20 at each position. Know there's usually a run on the top running backs, the top 2 QBs, and the top WR in the first round. The second round is more of the same, more focus on WR and QB. Third round is when you'll see the top 2 - 3 tight ends go. Defenses can go as early as 4th but usually start in earnest in the 6th. I wouldn't draft a kicker or defense before you have the meat of your team (QB, at least 2 RBs, 2-3 WRs, TE). Create a strategy around your sheets that allows you to take better players in the mid - late rounds.
3) Avoid "by committee" situations. This means positions like QB or RB where you know two or more players could rotate in. Ex: RBs in Denver, QBs in Detroit, RBs in Minnesota, QBs in San Fran. Taking both Mike Anderson and Tatum Bell is a waste. You'll drive yourself crazy trying to guess who to start each week.
4) Keep an eye on rookies and sleepers in the mid rounds. Ronnie Brown, JJ Arrington, and Carnell Williams are some of the rookies expected to start and make a splash. Imagine getting one in the mid-late rounds who breaks out mid-season for you!
5) Wait on the QB. Outside of say Manning and Culpepper, the rest can be had in rounds 3 - 6. You can stock up on RBs or an RB and WR in rounds 1 & 2, while usually still able to grab a Green, Bulger, Favre, Collins, or Brady in later rounds. Except if you start 2 QBs. Nothing like picking up Bulger in the 5th or 6th after drafting studs at RB & WR.
6) Expect the unexpected. Toughest part, but usually one of the top 5 RBs will be hurt for a considerable amount of time, one of the top 8 RBs will extremely outplay his draft position, and some one on offense will explode for a peak year (Manning in '04, Ahman Green in '03, etc). There will be players that probably won't last a full season (Foster in Carolina, Anderson in Denver), players that won't play to potential (Mike Vick, David Carr), and then there'll be older vets that slow down in the second half (Curtis Martin, Warrick Dunn). Knowing some of this ahead of time helps you anticipate needing backups and preparing for the eventuality. Having someone's backup (LJ for Priest Holmes, for example) helps in case the starter goes down.
7) Play the free agent/waiver wire on Sundays. Whenever you can, be near a computer on Sundays. You never know what big star will be injured. Grabbing the replacement (see Larry Johnson in KC) off of waivers could mean the difference in the season. Billy Volek, Nick Goings, and Larry Johnson were backups that came in and led their teams in late season play in '04. All were undrafted in the majority of leagues.
8) Watch the schedules. Fantasy playoffs are usually between weeks 13 - 16. Knowing your stars (or defenses) could have great matchups in the last few weeks helps to propel you to the title.
That's it for now. Stick with your gut, do some research, and good luck on draft day.