Auto throttle is armed pre flight. Usually LNAV and VNAV too (possibly operator dependant as previous post mentions, SOP is to arm both for my outfit). When you take off, you bump thrust up to 40% then hit TO/GA button, you (hopefully) get whatever thrust you asked for in FMC, defaults to all of it if you didn’t. Auto throttle engages in N1 mode. Pitch mode becomes TO/GA. No roll mode (LNAV remains armed if you armed it). At 84KIAS auto throttle changes to THR HOLD (thrust levers can be manually positioned). At 50 feet RA LNAV engages, at 400ft VNAV engages. At 800ft auto throttle goes into ARM mode and then at whatever thrust reduction altitude you have programmed it engages in N1 mode and reduces thrust to whatever climb setting you have programmed. You can engage the autopilot above 400ft.