A common (but not the only) way to go about this is to:
1. Determine the league cash pool.
(12 Teams * $260) = $3120
(12 Teams * $23) = $276
Assuming a $1 player minimum and 23-man rosters we know that each team has to spend $276 so we'll go ahead and take this out of the equation.
$3120 - $276 = $2844 <- Cash pool
2. Determine your hitting/pitching split. In a perfect world it would be 50/50 but projections are rarely perfect so we'll go with the standard 66/34 for sake of argument.
3. Determine your category splits. For ease of the example I'm just going to split the cats (mostly) even but you can weight them based on confidence just like you do H/P splits.
4. Determine the baselines for each category for each position used by your league. If your league uses 12 starting 3B than the baseline for each cat will be the 12th best total. In the case of C (where you use 2) it would be 24. This becomes a little more complex when you have overlapping positions such as CI or UT but I'll keep this simple.
5. Every player's preliminary value at each category will be their production minus the baseline at their position. If a player spans multiple positions he will have multiple values. An easy way to handle the ratios (take AVG for example) would be (Player AVG - Baseline AVG) * AB. There are other more complex ways to go about it and I believe there are links to posts about it in the FAQ.
6. You can add all of these VORPS and use it to sort each position list. This will give you a preliminary ranking for each position and will tell you who all the draftable players are at each position. Now you want to create a master list of these draftable players and get master totals for each category.
7. Let's that we have 14 hitters for 12 teams so you want to sum the top 168 values for each category. You'll do the same for pitchers. We'll say that top 168 HR totals adds up to 3,850. We already determined that we are allotting $375 to the HR category.
$375 / 3,850 = ~.10
If last season we had correctly projected Adrian Beltre at 48 HR and had know that the baseline HR total for 3B would be 25 than in this scenario would have estimated Beltre's HR total to be 23*.10=$2.30. If you do this for each category you can than add those dollar amounts and get a total dollar value.
Couple of notes:
As the draft goes on these numbers are going to fluctuate (draft inflation/deflation) based on how your league is drafting. You really need to set it up in Excel/Calc or use draft software to see this in action.
Your going to pay face value or even higher for the highest tier players but for the most part you do not want to pay dollar amount for each player. A good rule of thumb is to shoot for 75% of your projected dollar value. This serves two purposes. For one it hedges your projections a bit and the further we get away from first round material the less accurate (normally) the projections become. Two, if you overpay for a few studs and then underpay for a majority of your roster you'll normally be in very good shape (unless your projections are just whack
EDIT: That article posted by mamorris pretty much covers what I was trying to get across. Probably does a better job of it too.