1) Define your mission. Depending on what you want to do, the plane you'll need to do it varies. This includes distance traveled, weight requirements (people/baggage), speed, weather requirements, etc.
2) Figure out what you can afford. I think a good number of us would go get a Falcon or a King Air if we could, but we can't (I'd get an MU-2). Make sure to include all costs of ownership - remember that purchase price is just what you pay to play. It doesn't take long to spend way more than purchase price on your operating costs.
3) 1 + 2 = 3, figure out what plane you want to buy (the specific type).
4) Find an individual wishing to sell an airplane of that type.
5) Do a thorough pre-buy inspection. Determine what sort of condition the plane is in and whether it is a good option at a fair price. The answer may be no, in which case walk away and look at several others. By this point you should have a clear vision of what you're looking for.
6) Buy the plane, enjoy!
Note that it's more complicated than that, but to me those are the rough steps. You also need to line up financing (assuming you don't purchase the plane outright in cash), find insurance, figure out if you're insurable, get the appropriate training, etc. For me, there's a lot of research and speculation that goes into what I want to buy. Then I look for a beater that I can get a good deal on, as I want to be involved in the repairs myself and take advantage of them being done the way I want. Worked out very well for me on the Aztec.
