You need to have a small bit of relief or clearance in the middle of the fingerboard so that a vibrating string has ample clearance to vibrate freely and naturally. This is achieved by adjusting the truss rod. Most manufacturers will ship a truss rod wrench with the guitar. At any rate, you need to find the correct wrench for your guitar. Gibson guitars commonly use a 5/16 wrench, while Fender's typically use a 3/16 or 3/32 allen head wrench. The directions below apply to guitars with the truss rod adjustment located in the headstock only. Some guitars have the truss rod adjustment located at the end of the fretboard near the pickups. Since I've never done this type of adjustment, I can't give you the details, though the mechanics should be basically the same.

Don't ever force the truss rod if it doesn't move freely, this will most likely only result in damage to your instrument. If the truss rod doesn't move freely, bring it in to an experienced repair-person and have it checked out.

Tip: To quickly check whether the truss rod needs adjustment, hold the low E string down at the 1st and 13th frets, then tap the string down at the 6th fret. You should hear a light click as you do this from the string hitting the frets. If you don't hear it, the neck needs more relief. If it's extremely pronounced, then you probably have too much relief.

If there's a plate covering the truss rod, remove it to expose the truss rod. The following is a rough guide for setting the action:
Style of playing

Type of action desired

Relief in inches
Rock & Roll Medium - Low 0.010
Jazz Medium - Low 0.013
Acoustic-Electric Medium - Low 0.013
Classical-Electric Medium - Low 0.023
Electric Bass Medium - Low 0.020

In general, this measurement is taken by measuring the distance between the bottom of the string and the top of the 6th fret while holding the string down at the 12th fret and the first fret. This is where the capo comes in handy - put it on the first fret so your hand is free to take the measurement. Using a feeler gauge of the desired height, in this example, 0.010, hold the low E string down at the 12th fret (with the capo on the first fret), and measure the distance between the top of the 6th fret and the bottom of the low E string. If the distance is greater than the desired relief, then you need to turn the truss rod clockwise (towards your right) as you're looking down the headstock towards the body of the guitar. If the distance is less than the desired amount, then you need to turn the truss rod counter-clockwise (towards your left) as you're looking down the headstock towards the body of the guitar. The basic rule is:

* Clockwise to tighten for less relief
* Counter-clockwise to loosen for more relief

When making truss rod adjustments, always work in small increments, never more than an 1/8th of a turn. If you really have to force the truss rod, or it feels like it won't move, stop immediately and bring it to an experienced repair-person -you may have other problems that need to be resolved. Finally, always check the relief while holding the guitar in playing position. Otherwise, the neck can flex from the weight of the body if it's improperly supported. It's common for the truss rod to take a while to have it's full effect on the neck, so make sure you periodically revisit the relief to insure it's still accurate during the remainder of the setup process. Paul Reed Smith guitars use a double-acting truss rod in post 1992 production guitars. As stated on their web site: "PRS switched over to the double acting truss rod about halfway through the 1992 production year. To determine whether your guitar has this system simply examine the adjusting nut. The single acting rods used a brass adjusting nut threaded onto a steel rod. The double acting rods use a steel nut fused to a steel rod. The double acting truss rod achieves twice the amount of adjustment as the single acting rod with the same amount of movement of the adjusting nut. Do not over-adjust!"

Tip: You might want to consider doing this adjustment, and then allowing the guitar to sit overnight and adapt to the change. Then check the next day and make final tweaks before continuing on with the rest of the adjustments. It's also a good idea to check the truss rod adjustment several times during the setup, especially if you dramatically raise the height of the strings at the bridge, just to make sure it's correct.

Other thoughts: There are alternate methods for adjusting the truss rod/neck relief. For example, PRS recommends fretting the 1st fret and the last fret, then making the measurement from the top of the 8th fret. For most guitars, the truss rod really affects the area from the 1st to the 13th fret which is why the measurement is commonly made using the 1st & 12th fret. Try the different methods and see which one works best for you. Personally, I rather like the way PRS recommends doing it, and often, I'll use their method to get the neck close to the desired adjustment. It's something that you'll eventually get a feel for when your relief is set correctly, and you won't have to measure, you'll just know by the way the guitar plays.

Specifics for Gibson Guitars

Here's the actual answer I received from Gibson regarding the truss rod adjustment:
"We don't actually have any published specs for this. It actually is whatever setting works best for the guitar to create minimal buzz and good action." From my own experience, I've found that .010 is a good starting point on my Gibsons. I use .011 - .052 strings on all of my guitars.
Specifics for Fender Guitars

Fender recommends that you place a capo on at the first fret, and hold down the string at the last fret, then measure the distance between the top of the 8th fret and the bottom of the sixth string.
Neck radius Relief (at 8th fret)
7.25" .012"
9.5" to 12" .010"
15" to 17" .008"

* For PRS guitars, visit their website.