Why is that so great?
Working the wheel in Sector 2 is more important than in Sector 3. In fact, many people only do it in Sector 2. The reason being to unlock all the mutation lines. The extra AP are good, too, but most will want all the mutations. The easy route, which you might as well take, is the Sector 2 only spin/flip.
How it's done
There are two methods: the wheel flip, and the wheel spin. The first requirement for both methods is to decide on a stopping point which will be the character's final chosen faction. When flipping the wheel, one starts with one's arch rival faction and does all of the AP and mutation missions. All mutation quests are also AP quests, so if you do all the AP quests, you're covered. It is very important to only do the AP and mutation quests. Any other quests that give you faction points at this stage are bad. These faction points will need to be grinded away later, and each point you get puts you two points in debt with the opposing faction, which you are likely considering as an eventual ally.
Firstly, there is the wheel spin in which you will work your way around the wheel toward your ultimate goal. In other words, you will start with a faction allied to your chosen faction, and move away from that point on the wheel. Let's say you want to be an Enforcer. You would start by doing either the Tech or Lightbearer missions and then go on to the next ally from there. This requires many shorter grind sessions between factions. It is easier to grind for faction points when your primary faction is lower. However, stopping to grind faction will happen more often, and so will traveling. Spinning the wheel sounds like the most efficient way to do it at first, but it's far more time-consuming than a flip when you factor in travel times and time spent grinding. And if you are doing a wheel spin and want to get the Sector 3 AP, forget it. Human beings don't typically live that long. If you want the Sector 3 AP, you have to do a flip.
The wheel flip is basically a huge grind across the wheel. You start on the opposite side of the wheel, rather than adjacent. You then do all of your enemies' faction and mutation missions (immersion-breaker, I know) in Sector 2. Then you do all the non-faction missions in Sector 2 and 3. You will still need to grind a few levels to 35 to start the enemy missions in Sector 3. You then go back to Sector 2 and start your grind across the wheel. During the grind across, you will, at some point be hated by all the factions (see right), but don't panic. Once your favored faction no longer wants your head on a pike, you may play the game like a normal person once again -- the way the developers intended it.
This is the worst part. Once your faction wheel has a blowout, you need to patch it up. The wheel spin requires a bunch of small grinds, whereas the wheel flip requires one epic grind session.
There are four ways to gain faction points: one time missions, repeatable missions, killing mobs, and PVP . The repeatable missions sound like the way to go, but they are all in PvP zones and all have a faction point or level cap. What's so bad about PvP zones? Well, aside from the obvious, you can lose a lot of faction in PvP if you are not careful. If someone from an allied faction decides to kill you (it happens often), you had better just let them do it. The penalty for dying is much less severe than the faction hit you will take for killing them. But if you can endure the fraticide and possible griefing that may occur, then its typically your best method. Trying to gain faction points by simply PvPing leaves way too much to chance, as you may sit there for hours and never find a single enemy. So that leaves mobs.
Grinding the mobs
The way most players grind faction is by killing mobs. For some factions it is a walk in the park -- for others, the mob grind is a nightmare. The good news, however, is that when you get to a mob camp there are usually other players doing the same thing. They typically form groups and kill mobs in shifts, as one player can usually kill them faster than they respawn. If you are still up in the air about which faction you would like to befriend, consider the ease of wheel flipping. In order of easiest to hardest: Lightbearer, Enforcer, CHOTA, Traveler, Vista , and lastly Tech. Both Vista and Tech are very limited in faction grinding potential, and you had better be absolutely sure they are the faction you want to end up with, because it's going to be a long ride.
The future of the wheel
Well frankly, it looks bleak. The developers have already made it a little less attractive by requiring positive faction for faction specific abilities. Also, the mob grinding has been made more tedious than it was before. Flipping and spinning the wheel is already a chore, and if you plan on doing it, you had better do it soon.
I'd also like to add a fond farewell to Lee Hammock. The Fallen Earth community will miss him, and I wish him luck in all his future endeavors.