Without wishing to cause a riot, Tootles, when you do your first 6 Take off and Landings in a 737, or for that matter any jet (unless you can get Zero Flight Time, but I digress) on your first type rating, you actually do Touch and Go's.
For the most part, you would normally have two crew when you are flying the Line, the FO normally gets to hit the TOGA (Take Off, Go Around) Buttons on the Thrust Levers after standing them up, then lets go to hold the Control Column, the Capt is in charge of them on the T/O run. On landing you do your own Thrust and then Reverse, Reverse Idle normally for me anyway, then at 60Kts the Capt will call 'I have control' and you relinquish control to him for the taxi in.
Hope that helps
Tony