I'm getting into the autothrust world and I have the question of whether it would be possible to disengage it and select the thrust manually in a plane that already has autothrust. How could it be done? Maybe it differs from plane to plane.
You are correct that different planes operate slightly differently, but they are mostly pretty similar. Just as with the autopilot, the autothrust can be disconnected and the airplane can be controlled manually.
Below is an image of the Mode Control Panel on the 737 NG, which is located just below the windshield. The section that controls autothrust is located towards the left side. To disconnect the autothrust, you can just flip the "arm" switch to off.
Below is an image of a 737 NG cockpit, with the thrust levers located in the middle. With autothrust on, the levers are moved by the autoflight system to correspond to the autothrust setting. The levers can be moved by the pilots but the system will try to drive them back to the commanded position. Once autothrust is turned off, the system no longer moves the levers and they can be controlled by the pilot manually.
Airbus planes such as the A320 are a bit different. The levers do not move to match the autothrust setting, but autothrust can still be turned off to use the levers manually. The levers can also be pushed forward past the "climb" detent, which overrides autothrust to choose higher thrust settings.