Study, study study. This usually means looking at several cheatsheets, looking at (if not participating in) a few mock drafts, reading topics in the forum and getting other viewpoints.
You might want to take a peek at some of ESPN's live drafts as they are going on, at least the first 6-10 rounds or so. That is where you 'build' your team. Later round picks are usually for filling holes, taking a gamble on an up and coming player, taking the best available player, etc.
Be aware of different draft strategies like LIMA, 3 OF early, 'strong at the corners', 'strong up the middle', dominant pitcher strategy, etc. I've won leagues drafting 3 SP first, and won not drafting SP until like the 6th round.
I would say try to get 2 top SP, and 2 OF in your first 6 picks. I would not generally grab a RP in my first 6 picks.
SP's with high K rates and ERA's of 3 or lower are huge advantages to own. I try to anchor my staff with at least 2 of them, if you ignore SP early, you likely miss out on them.
Pedro, Prior, Schilling, Halladay, Hudson, Vazquez, Johnson, Wood, Oswalt, Zito, Beckett, Santana are guys I drool over owning. Gimme 2 of them in the first 6 rounds, and I'm, a pretty happy owner. Pedro might be worth a first round pick after pick 7, otherwise I wait until round 2. Prior thru Halladay are solid 2nd round picks. Hudson Vazquez maybe end of the 2nd early third. Johnson and Wood are solid 3rd rounders. The other s should be picked up around round 4 or 5, with Beckett and Santana maybe lasting until round 6.
There are still many good SP after them, but these are the guys I put at a premium this year. I may have forgotten a couple, but Schmidt and Moose were left off intentionally (injury, and not a personal favorite respectively)
* Steroid induced record