You can certainly do a kind of VO2max test at home. A true VO2max test requires the kind of equipment you see in the photos; cyclist breathing through a mouth piece connected to tubes that run to a large machine that analyzes the gases moving in and out of the body. However, if you have a power meter and you perform the protocol correctly (a Computrainer helps here), there is a very close relationship between oxygen consumption and MAP (maximal aerobic power) such that VO2 can be calculated via a simple mathmatical formula. However, it is your MAP that is of more use to you as a cyclist in terms of assessing fitness, applying the test results to the real world and for deriving training levels.
Check out this link:
http://www.cyclecoach.com/articles/?article=Power_Guidelines&ext=.htm
It will describe the test for you in more detail.
Should you want to perform a laboratory VO2max test in order to directly measure VO2 kinetics, try your local university or sports medicine clinic. This will cost you a lot more than doing it at home as well.