So the movies clearly show Saruman taking Gandalf's staff away from him when they fight. The books I don't think are explicit in this but it is reasonable to assume there as well.

How does he get it back after he escapes?

The whole bit about the breaking of Saruman's staff, as well as his comment about Gandalf wanting the rods of the 5 wizards, and Wormtongue's orders about the staff all indicate that a wizard's staff is not just a piece of wood.

Do you reckon a wizard can make himself a new staff? What?