Assuming wave-function collapse is correct (which can be a relatively hefty philosophical claim in some circles), then think of measurement this way:
When you measure an observable on a system, you collapse the wave-function of the system into a Dirac delta function in the eigenbasis for that observable.
If you measure position, you get a delta function in position-space. If you measure momentum, you get a delta function in momentum-space (or a sine wave in position space). If you measure energy, you get an energy eigenfunction.
Then - after the collapse - the system begins evolving according to Schroedinger's Equation once again, but this time your initial conditions for the system are whatever shape you collapsed the wave-function into with your measurement.
Remember, particles obey Schroedinger's Equation. It tells you what they do in Quantum Mechanics - just like Newton's 2nd Law tells you what they do in Classical Mechanics. Give me the Hamiltonian and the initial conditions of a system, and I will tell you how it evolves in time. That is the name of the game for much of Quantum Mechanics.
(As an interesting side-note: if you make another measurement of the same observable very quickly after making the first measurement (and I mean VERY quickly), you will get back the same result because the wave-function has not had time to evolve away from that state yet.)