How to Service Embroidery Machine

Technitions grease, oil, any moving parts that are usually not user servicable on their own.
They check for wear and tear and advise on part replacement.
They check and clean sensors that are used to control the timing and positioning of the machine which are usually optical encoders which can collect dust and cause errors.
They check the mechanical timings of the hooks, the needle depths and they put it through test modes that a trained tech can spot issues with solenoids, motors ect before they break down completely.
Sometimes they adjust back end settings that are used to callibrate the machines motors ect. But rarely.

Over time machines wear down or parts slide out of place just slightly due to any number of common issues such as birds nests, needle breaks ect. And the machine can get kinda sloppy, So you have to have a tech come and tune up any of those parts and if they are a really good tech, they tune the machine to itself to run optimally instead of tuneing it up by the book

Are you trying to do this as a service tech as a job or you want to service your own machine?
There are ways to learn by reading and trial and error, buying a service manual reading the user manual but honest to god training is usually by barudan and you would have to call around there and it would probably be a paid training.
That said troubleshooting is a skill unto itself. If you are skilled in troubleshoot and repair than I'd say its worth getting the service manual for your own machine...

I do both. I pay a tech and I do my own troubleshooting and repair. There are always tricks that you need the manual and a full time tech know that even a book or instruction sheet won't tell you.