The ship will coast up to the higher orbit. If nothing is done, it will coast back down again. So fire the engine again, so that the orbit is circularized at the higher level.
This is called the Hohmann Transfer Orbit, or the Hohmann Ellipse.
For Orbital Rendezvous, which is the ship trying to meet an object in a different orbit, it gets interesting, because you have to time the engine firing so that the ship and the object arrive at the same point at the same time. For example, a ship travelling from Earth to Mars has to wait until the two planets are in a suitable position.
You have a limited time to fire the engine to start the journey before the planets are no longer in the correct position. This is called the launch window.
This simulation shows how a ship might use the Hohmann Transfer to travel from one planet to the other, waiting until the launch window arrives.