The rules don't give a very good intro to F-Class, or any NRA discipline. You kind of need to have an idea of what they are trying to do before the rules make much if any sense at all.
General concept: You shoot at a target that is, for the sake of this example, 600 yards away. The center ring or 'X' ring of the target is ~3" in diameter. The next ring out is the 10-ring, and is 6" dia. The 9-ring is 12", etc.
The targets stick up over a protective berm, behind/below which they can be pulled down and scored, then ran back up.
Targets up, view from 600yds
View in the pits, targets down
You fire a shot, after which the people in the pits pull the target down, put a spotter (the white disc with the spindle, shown in the first picture) in the bullet hole, and hang a value marker (the orange disc in the lower left corner of the first picture) around the outside in locations that correspond to your score for that shot (if a shot is near a scoring line, its hard to tell whether its a 10 or a 9 from several hundred yards away, even with good glass), and then run it back up.
On the next shot, the person scoring your target will pull it down, remove the spotter from the previous shot, put an appropriately colored paster over the hole, and put the spotter in the new hole, move the scoring disc and run it back up. The whole process *should* take 10-15 seconds per shot.
This process is repeated until you have the required number of record shots 'for score' or you run out of time. There are a few variations on how many shots and how much time, but for this example, you get two 'sighting' or 'sighter' shots (freebies for getting centered up on the target - they don't count towards your score) and then 20 'record' shots for score. The time allotted is generally at least 1 minute per shot, or 22 minutes (2 sighters + 20 record shots). You can shoot as fast or as slow as you want - if your target puller is healthy and fast, you might be done in under 5 minutes. Or if the winds are changing direction you might take 21:59 to shoot in... but at 22 minutes, the targets get pulled down and stay down whether you are done or not!
Who shoots, who scores, and who marks the targets when, etc. is referred to as 'squadding'. For a normal 600yd match where you shoot three times @ 600yds (3x600), ideally the match director will assign people to 3 relays, with one person per relay on each target. Starting out, relay #1 goes to the firing line, relay #2 sets up a spotting scope (or binocs, but trust me, even a crappy spotting scope beats holding up binocs) and folding chair behind their shooter on relay #1, and relay #3 heads to the pits to pull targets. Relay #1 shoots, #2 scores for them (writes their scores down on the score card), and #3 pulls.
Then once the line is made safe again, relay #3 comes out to score, relay #1 goes down to the pits, and #2 gets ready to shoot. This is called a 'pit change', and will happen several times throughout the day so everybody shoots, everybody scores, and everybody pulls targets.
So at the end of the day, you'll have fired 66 shots - 2 sighters and 20 record shots, x 3. While the shooters put the targets away and clean things up, the match director will be tallying the scores (either manually or on a computer) to see who won, who got second, if there were any special categories like Junior (shooters under 21) that bear recognizing, etc.
Now that you are probably thoroughly confused
we'll cover the guns: there are two equipment 'classes' to F-Class - Open and TR. Basically... Open is unlimited caliber (under .35 cal), front rest allowed, rear bag allowed, no brakes, under 22lbs for the gun as you pick it up of the rest.
TR is .223 Rem or .308 Winchester from a bipod (or sling), rear bag allowed, under 18lbs ~2 oz as you pick it up off the ground (including bipod or sling).
Rifle must be fired from the shoulder (not free recoil), from the ground in the prone position.
Usually there is a minimum number of shooters (5) before match directors will split F-class into 'Open' and 'TR' for awards. If there are only six shooters, everybody is generally lumped together and everyone is essentially shooting 'Open' regardless. At larger matches (regional or national championships) is where you'll almost always see the classes split up as there are plenty of shooters in both groups.
Matches can be shot at different distances from 300yds to 1200yds, with targets sized accordingly for the distance. Some matches may have you shoot at three different distances in one day, say 300, 500, 600yds, changing firing lines between each relay. Others may have people shooting other variations such as 'pair fire' where the shooter and scorer set up on the line side by side, alternating shooting and scoring. Details like that are what the rule books are for, and you'll quickly get the hang of it by going to matches. For now, the above should get the general idea across.