Take the best player on the board, regardless of position, then make trades from your position of strength.
Another problem with this strategy is that the player's VALUE isn't important, it's his PERCEIVED value.To give a somewhat extreme example... let's go with Mike Anderson last offseason. Let's say you thought he was far and away a top-10 RB (and therefore had a value on par with a late first round selection). The other owners in your league disagreed, and so he slid to the 16th round, where you gleefully snatched him up. Good luck trying to shop him. Even if you're in a trade happy league, the fact that you got him in the 16th means the owners don't VALUE him higher than a 16th, and so they'll only trade you 16th-round value for him.
Now, let's say you think that Andre Johnson is a total turd last season, but he slips to the 16th (mostly because everyone's drunk and not paying attention). You have a choice between Anderson (stud) and Johnson (turd) in a trade-happy league. The smarter move would be to grab Johnson, since his PERCEIVED value was so much higher. Even if you think he's a turd, you could GET a lot more for him. For instance, you could ship him off for a 7th or 8th round player and probably get Mike Anderson thrown in for good measure.
Which brings me to my huge draft strategy. KNOW YOUR LEAGUE. KNOW COMMON OPINION. Disagree with it, absolutely, but KNOW it inside and out. You have to know who's going to go where. Also, keep track of how many players at each position each owner has.
An example. Let's say that you have the #2 rated defense as a 14th round prospect, but you know that the rest of your league is going to start looking at defenses in the 10th round. If the 12th round comes around and someone grabs the 1st rated defense, then it might not be a bad idea to "reach" and grab the #2 rated defense right them. Yes, you are grabbing it higher than you have it rated, but if your league really goes into a long run of defenses, then you actually didn't lose any ground in draft position (it's like you just held the 14th round of the draft 2 rounds early).
Okay, now an example to the opposite side. Let's say you have the #1 rated defense as a 10th round prospect, but know that the rest of your league never picks up defenses before the final 4 rounds of the draft. Well, in that case, ignore the fact that your board is saying that this defense is the best pick available, and let it slide to the 16th or something. You still pick up your defense, but the cost is a lot less.
That's a pretty basic summary of knowing common opinion... but knowing your league's needs can be a very powerful tool.
For instance, I draft in a league that has roster limits on the draft. Everyone MUST draft 4 QBs, 6 RBs, 6 WRs, 2 TEs, 2 PKs, and 2 Defs. If everyone else in your league has drafted 6 RBs by the 12th round, and you only have 4, you can ignore that position entirely until the final 2 rounds of the draft, since no one else can take an RB. The exact same players will be available then as are available now, so spend your time grabbing WRs, or QBs, or whatever. Paying attention to the number of players left in a tier and the needs of the teams drafting before your next pick also gives you a very good way of knowing if you can let a particular player slide without worrying about the league snatching up the entire tier (and thus forcing you to take a reduction in value with your next pick).
The entire goal behind working the draft as opposed to just drafting based on your board is a chess concept. Ever pick should do two things. It should benefit your team as much as possible... but it should also gain you a *TIME* advantage. The whole concept of Time in chess pertains to developing as much of your pieces as you can without compromising your position of strength. In a draft, it's much the same theory. You want to develop your roster as a whole as much as possible without sacrificing on value.
The theory behind gaining "Time" in a draft relies a lot on tiers. The later you can grab a player without dropping a tier, the more "time" advantage you gain. So if you grab a high 2nd-tier WR in the 3rd, and I grab a low 2nd-tier WR in the 6th, you may have gained more player value than I did on the deal, but I gained a ton of "time" on you.
A lot of emphasis is placed on quality of projections, and that is indeed a very important componant of the draft, but I guarantee you that if your projections are slightly better than mine, and my knowledge of you and the rest of the league is drastically better than your knowledge of me and the rest of the league, I will "beat" you in the draft 10 times out of 10. I will get more value than you do, and I will get it later than you do. As an example... let's say we're in a guppy league where everyone sluffs 2nd RBs until the 8th round. You go by your board and draft 5 top-24 RBs in the first 5 rounds. I go by my knowledge of the league, and snag myself a pair of top-12 RBs, but then fill out my roster by "reaching" on QBs and WRs who probably shouldn't be going until the 10th. The result? You're stacked at RB, but by the time to get around to QBs and WRs, you're left with scrubs and borderline starters. I'm stacked at RB (although not as deep), but have quality QBs, WRs, and TEs... and then when the rest of the league turns its attentions to RBs, I can quietly add a little bit of quality depth at a much better "time" value than you did, adding RBs of the same tier several rounds later than you got yours. To add insult to injury, I can then offer to trade some of my "scrub" players that I "reached" on for those studs you were drafting, and you'll be forced to accept, since you're entirely lacking that position. I mean, imagine the horror you would feel if you were loading up on RBs in the first 8 rounds while the rest of the league quietly drafted 36 QBs.
In short, don't neglect the human element of the draft. It's possibly the single most important aspect of all.