How do I make a height adjustable desk?
I've built this desk twice. It costs me ~$100 USD in materials:



And here is my version of the desk:



You can adjust it, but it is a little difficult.  However, you can fit a modified treadmill under it as you can see in this video of me using the desk.  I'm able to type comfortably while walking at 2.2 MPH.  

If I may presume that the reason you want a height-adjustable desk is so you can sometimes sit and sometimes stand ( or walk!), then take the idea of height-adjustable and flip it on its head.  Just buy a tall chair instead.  (I only have a stool at the moment):



I have a height adjustable desk at work ( not ghetto'ized, like my home version).  The linear actuators for my desk come from LINKAK: