A lot of the directives you’ll hear will be a standard phrase followed by a number. “Climb and maintain,” for instance, is an instruction to your pilot to climb to a given altitude and then stay there, so “climb and maintain 5,000” would mean they should commence climbing in altitude and then, once they’ve hit 5,000 feet, level off. “Turn right at 090” would mean the tower has assigned your pilot a new heading of 090 degrees, and they need to make sure they get there via a right turn and not a left turn.
One of the phrases you’ll hear crop up most often is “cleared for takeoff,” which means exactly what anyone of sound mind would assume it means. Another common one is “line up and wait,” which means a tower controller is telling an aircraft to get onto the runway (line up) and then wait (that bit where you’re out there just sitting, a time which used to be dull but is now filled with Interesting Recordings). Then you’re cleared for takeoff. The reason you have to wait sometimes is because there might be crossing traffic on your runway, and you obviously want any other aircraft to be safely on the other side before you get started.