For those of you that are Stihl confused:
There are 4 right thumb lever positions on any Stihl saw.
Full choke on any Stihl is the lever pressed all the way down. That is also called the cold start position. It is for cold starting only, and only good until the saw rumbles over, pops, or fires. Any more tries to start in this position after that happens and it will just flood.
Fast Idle on any Stihl is the lever pressed one up from full choke. It is also called the half choke position. It is good, as Tommy says, for starting a warm saw. You use it to start a cold saw after it has popped over on full choke. You can usually use it to start a hot saw as well. If you throttle the saw from this position it will automatically pop into the run position.
The run position is the lever pressed one down from kill. This is where to put the lever when you start a saw that is warmed up. This is also where the lever will wind up if you press the throttle with the saw in either of the choke positions.
The kill position, or stop position is the lever all the way up. This shorts out the ignition and causes the saw to stop if it is running. It will also keep the saw from running, no matter how many times you pull the starter cord. I call this the 'dumb :censored:' position, as I have tried to start a saw more than once with the lever in this position.
One good thing about Stihls that I like is that every one of them (at least the newer ones) have the same thumb lever. Every one starts the same way. The 0xx models seem to start easier, and they will usually run from the full choke position long enough to pull the throttle without having to pull the starter again on fast idle.
Now for the underground guide to starting Stihl chainsaws (everyting that OSHA does not want you to know or do):
First is the chain brake. Lever forward, the chain brake engages. Lever back, and it releases. Several here have different methods. I used to start saws with the chain brake set, but I no longer do that. Reason being that when you start the saw at fast idle, it wants to run, rather than bog down with the chain brake set. Its hard on the clutch when the saw bogs down. The engine wants to run as well, and you want it to run in order to start and warm up. I use the brake when walking with the saw, handing the saw off, or setting it down. I also engage the brake when the bar is flying at my head in a kickback. Just be aware of proximity when starting your saws with the brake off. These are dangerous tools, if no one told you by now. If someone is close, or I am in brush, I will start the saw with the brake on. But that is an exception. I also prefer the mind set of thinking that the chain is free. When I used to start my saws with the brake on, and forgot to set the brake now and then, it was an unexpected surprise. You do not want surprises when starting saws. I also have saws that do not have chain brakes (ie., older Mac and Olympyk). So one standard method works better for me.
Second in this lesson is drop starting. The book explains for the fist 8,000 pages how to start a saw on the ground. This is great for making OSHA happy after years of law suits. However, many of us, myself included, believe that it is actually less safe and harder to start a saw on the ground. Chainsaws were originally (and still are, actually) designed to start in your hands, standing up. To do a proper drop start, you hold the top bar in your right hand and starter in the left. Hold the saw to the front/left side of your body. Then you pull up on the starter recoil with your left arm while lowering the saw with your right. This is actually easier on you and your saw, becasue you are standing in a balanced position, and no leaning down in an akward position with your foot in the handle of the saw. This starting position also makes it easy enough to start the saw without a decomp button. My 044 does not have a decomp, and I can start it without any real problems (even with a bum left arm that has tendonitis really bad). An alternative to the standard drop starting method is to hold the saw handle between your knees, and pull the starter with your left hand while holding the top handle in your right hand. I find this akward though, and prefer to let the saw swing free to my left.
So finally, to answer the question, why is there a decompression valve or button (commonly called 'the decomp' here)? Several reasons. One is that starting a saw on the ground is a lot harder and the recoil can snap your wrist good and hard in that position. Another is that some people are not as strong as others. Another is that it is easier on your arm and wrist to use it. The decomp is sort of a follow-on to the OSHA requirements for starting a saw on the ground. Anyway, using the decomp can lead to flooding when cold starting a 361, and so it is not advised to use it when they are cold. If you drop start your saws, it is not really as required, though I find it is easier on my saws and me to use them when hot starting my saws.
OK, OSHA can flame me now...