The exact details for the autothrottle system obviously depend on the aircraft. I will focus on the Boeing 777 as an example here.
The B777 FCOM (Flight Crew Operating Manual) describes the thrust lever operation like this:
Autothrottle Thrust Lever Operation
The autothrottle system moves either or both thrust levers to provide
speed or thrust control, depending on the active mode.
Thrust levers can be manually positioned without disconnecting the
autothrottle. After manual positioning, the autothrottle system
repositions thrust levers to comply with the active mode. The
autothrottle system does not reposition thrust levers while in HOLD
mode.
(Boeing 777 FCOMv2 4.20.9 - Automatic Flight - System Description)
The thrust lever block on the 777 looks like this:
[...] The servo motor/gearbox installation is located below
the throttle levers with direct mechanical linkage to the
levers via over-ride slip clutches. [...]
(D Wilkinson, Data Bus Technology Applications—Boeing 777 Autothrottle Servo Motor)
These over-ride slip clutches allow the pilot to move the thrust levers against autothrottle input. The use of such slip clutches is quite common, also for the autopilot (see e.g. this answer).
The internal components of the autothrottle servor motor (ASM) are shown in this picture:
The unit consists of a high efficiency brushless d.c.
motor, single-stage 9 to 1 ratio reduction gearbox and
output drive spline, together with the ‘smart’ control
electronics, contained in a support housing providing
the required ARINC 558 mechanical interface plus electrical interface via a pigtail cable and connector. [...]
The high efficiency brushless d.c. motor has an 18
pole stator with delta three-phase windings and a 6 pole
rotor using high energy samarium cobalt rare-earth
magnets. Three bi-polar latching Hall Effect sensors
detect shaft rotation for commutation and tacho rate
information.
(D Wilkinson, Data Bus Technology Applications—Boeing 777 Autothrottle Servo Motor)