The Heisenberg Representation of Quantum Computers (Daniel Gottesman) http://arxiv.org/abs/quant-ph/9807006
Suppose we have a quantum computer in the state $|\psi\rangle$, and we apply the operator $U$. Then
$U N |\psi\rangle = U N U^\dagger U|\psi\rangle$
so after the operation, the operator $U N U^\dagger$ acts on states in just the way the operator $N$ did before the operation. Therefore, applying $U$ to the computer transforms an arbitrary operation $N$ by
$N \rightarrow U N U^\dagger$
For the first step, I understand that placing $U^\dagger U$ on the right hand side has no effect; it resolves to the identity matrix.
I follow what the text is saying about considering the the right hand side as applying $U N U^\dagger$ after $U$ has been applied to the state.
I don't quite follow the result for how the observable $N$ is changed when the operator $U$ is applied: $N \rightarrow U N U^\dagger$. I'd appreciate it if someone who "gets" it could put a little more explanatory text between the two steps.