Before installing a hyperdrive in a ship be sure to look up its L jump class (ie mass) and choose a jump engine that will work with its L class rating.

The jump takes place half way through the normal movement and is limited to one jump per turn. You can dock pods before HYPing. You only ever need 1 hyperdrive per hull. And combat can happen before then. (unless you have a fast HYP ship)

Privateer Meteor Class and Rebel Falcon Class are fast hyp ships, and jump before normal movement (phase 0) and have normal warp movement after the jump.

Hyperjumping ships can be seen better by enemy ships immediately after a Jump, and can be intecepted and attacked right after a jump. However the scanners of a hypership only work at about 25% normal range immediately after a Jump. So you tend to arrive semi-blind and highly visible.