Just a few further comments
Sabenapilot gave a good description of the system. I just want to add, that if the trust levers are in the TOGA or FLEX gate (with bth engines running), the autothrust system is not acitve, it is only armed. So you are always operating at a fixed thrust setting. Once the thrust levers are moved to the CLIMB detend, the autothrust system is activated and the thrust lever position gives the upper thrust limit for the autothrust system. If an engine failure is encountered, the autothrust system becomes active up to the MCT detent, which is the same as the CLIMB detent.
Yes it is that easy.
Just some examples the other way around.
Set climb power:
Airbus: Keep looking outside for traffic, just pull the levers back one or two detents.
Boeing: Stop everything else, look at the gauges, find the climb thrust value, set the levers accordingly. Look outside again.
Airbus: Just slam the levers forward into the TOGA gate
Boeing: Stop everthing else, look inside, carefully push thrust levers forward, don't overboost engines, look outside again. Or: start searching the TOGA-levers hidden somewhere on the thrust levers, pull them.
Now, before somebody starts to bash me because I am apparantely bashing B*****. I intentionally exaggerated a little. After some time on the airbus, you get a feeling where to put the thrust levers when disengaging the autothrust. So you pull the levers back, take a quick look to readjust, then disconnect.
When flying, I tend to disconnect the autothrust when deccelerating the aircraft, with thrust idle conditions. So all that you have to do is pull the levers back all the way and disconnect. The idle thrust condition can be checked without your view ever leaving the PFD (primary flight display), as it is shown there.