When you request take off clearance, remaining in the pattern, that mean you want do touch and goes. ATC will give you clearance for take off with traffic direction:
"Xx, runaway 31R, cleared for take off, make right traffic"
Thet mean you must turn right after teke off on right crosswind, then right downwind, right base and on final runway 31R.
Once when in the air, ATC should sequence you:
"Xx, nbr 3, traffic to follow is on right downwind"
That mean two airplanes are in front of you and you need to follow that one wich is on right downwind.
ATC will send clearance for option
Xx, nbr 3, runaway 31R, cleared for option"
That mean you have clearenc for lending and touch & go for runway 31R, and after t&g again follow right traffic.