How do I desolder a component, a small component with a hot air gun? WIthout breaking it? And also if that is not the right way to desolder, what is?
No, not a hot air gun.
Use a soldering iron, and either a solder sucker (suction device), or solder wick (wire mesh that soaks up solder).
How many leads are you needing to unsolder ?
There are special "hot air guns" specifically for soldering. They are known as "Solder Rework Stations", and blow very hot air (~300-400C) through a very small nozzle. If you must use hot air (and for surface mount components it can't be beaten) then you really need to use a proper rework station.
Most rework stations cost hundreds of dollars, but there is a model around that is gaining popularity which is, not surprisingly, made in China, that costs considerably less. The make is "Atten" and the model I got recently is the 858D+, and it cost me about 50GBP. And I love it 
So no, don't what ever you do, try and use your Black and Decker paint stripper hot air gun - it will just kill your PCB.
If it's an SMD resistor or ceramic capacitor that you want to remove, then you can do it with a pair of fine-tipped tweezers and a soldering iron tip large enough to heat both pads at once. Otherwise, you need a hot air rework station.
We really need to know what component. Is it surface mount, or through-hole? Two leads, or 44?
Chip-Qik is essentially a very low temperature alloy. You wick or suck up most of the solder already there, then flood it with Chip-Qik. It stays molten for a long time, the idea is to get all of it melted at once. A few leads, just an iron will do it, for something like a 100 pin gull wing device you can warm it all up with a rework station hot air.
Depending on the component, the hot air gun simply preheats the components (or a hot plate) then using the soldering iron to finish the job...
If it's got more than 3 pins use tweezers and the hot air gun to lift it out if there's something near by that could be damaged there is tape you can buy to shield the components while using the heat gun...
If the component you are trying to remove, does not need to be saved, it may be easier to snip each of its pins, get it out of the way, and then unsolder/remove each of the pins individually.
How do I desolder a component, a small component with a hot air gun? WIthout breaking it?
Looks like he wants to keep it ..
One of my desoldering instruments for 2 leaded SMD components is sort of a set of tweezers made of two soldering irons hinged together. You can also get or make special tips for a soldering iron that are broad tips with a relief cut out of the middle, so it bridges the component and heats both sides at the same time.