We've talked a good deal about league parameters, owner tendencies and how to find bargain players, but a big part of doing well in fantasy leagues is mastering the player acquisition process itself. The vast majority of leagues apportion players to owners via auction or draft. Let's tackle some of the key considerations for each.
Auction
Typically, owners start out with a $260 budget with which to nominate and bid on players. In shallower formats, e.g., 12-team mixed leagues, the strategy is fairly simple: Buy 4-5 superstars with three quarters of your budget and then fill in the rest of your roster on the cheap. This works because the replacement value is so high that you'll have productive players at every position and huge difference makers to separate you from the pack.
But as league parameters get deeper, e.g., 12-team AL- or NL-only leagues, and the replacement value goes down, you cannot find reliably productive players for cheap. So if you're going to buy big stars, you'll usually be left with some scrubs. (This is the "Stars and Scrubs" approach). Or you can eschew star players for a portfolio that's more balanced across the board. (This is the "Spread the Risk" approach). The advantage of the former is you're getting huge production from a few slots, and if a couple of your scrub lottery tickets hit, you'll likely win the league. The advantage of the latter is you're far less likely to be derailed by a big injury, and every roster spot is far more likely to be contributing for you.
I personally use a hybrid approach where I buy some stars and my scrubs are mostly $3 - $6 players rather than $1 ones. Essentially, I think I can find more promising lottery tickets if I have my choice among the cheaper players who come off the board late. And I want to be able to buy expensive players I believe are undervalued. If you're committed to the spread the risk approach, you're barred from buying a player you believe is worth $40 even if he's available at $33. I never want to cut myself off from a potential bargain.
Finally, the hallmarks of a sound auction strategy are patience and discipline. While you want to win your preferred players, you have to be able to let them go when the bidding gets too high and squeezes your likely profit margin. You have to know who your next target is and consider which other owners need players at that position and what their remaining budget is. Sometimes, you simply have to go to the mat for a player given the remaining alternatives and pay what it takes. Sometimes you have to let him go and find multiple cheaper players to target instead.
Draft
While auctions require discipline and patience, drafts favor a more aggressive approach. My rule of thumb in a draft is: "Take the player you want unless you're fairly sure he'll be available in a subsequent round." That seems obvious, but many owners are wary of taking a player early in the second round whose average draft position is middle of the third. But if you're picking early in the second round, you won't pick again to late in the third, so this is your only chance to get that player. The average draft position is just the market value of a player, i.e. it's just a collective opinion that has no bearing on how that player will perform. The worst thing you can do is forgo the player you think is best for the one you "should" take based on ADP. In that case, you might as well set your rankings based on ADP and set them on "auto-draft."
Additionally, drafts require you to be aware of the plateaus and drop-offs at each position. If there are 10 second baseman in the third tier, all of whom are roughly equal, go ahead and take a slightly lesser player who might be one of the two remaining productive options at his position. You can always get one of the interchangeable second baseman later.
Finally, we get a lot of questions about whether one should take a hitter in the first round and a pitcher in the second, or when to take a closer. The answer is always: "It depends." Never go into your draft with a preordained plan to take particular positions in particular rounds. As many auctions and drafts as I've been in, I still never know what's going to be available to me when my turn comes up, and it's crucial to be flexible and allow yourself to reap unexpected values when they fall to you.