You don't measure the wave function, you measure the state of the underlying system (qubits or whatever). When a measurement is made, the wave function, which

You don't measure the wave function, you measure the state of the underlying system (qubits or whatever). When a measurement is made, the wave function, which gives the probability of finding the system in any particular state, "collapses" so all the probability mass is on the state you just measured. If you keep measuring the system quickly (relative to the time it would take to change significantly) you actually stop if from evolving the way it would have if you'd left it alone, as if you dropped a ball and kept staring at it and it dangled in the air instead of falling.