you're gonna need to show proof that you can speak german first.
you normaly apply to universities direction (except for North Rhine Westphalia i think where they have a system similar to UCAS)
process is individual from uni to uni, department to department and course to course. altho generally for engineerign courses at most unis you jsut have to show up and sign up. other than that most subjects have a NC (numerus clausus), which means you get in if you have a certain grade on your a-levles (which you'll need to get convertrted at the Zeugnissanerkennungsstelle). and the places on the course are assigned by academic merit only.
for some more fancy courses or units that consider themselves more facny, they have further testing. TUM i tihnk requires a letter of motivation, might even require an entrance exam for some subjects etc.
best unis for engineering subjects are generally the technical universities:
big names include:
TU Munich
Uni Karlsruhe
Uni Stuttgart
RWTH Aachen
Uni Erlangen also had quite a good reputation.
generally employers won't care however what uni you are from, as they noramly consider all unis to be equal. (we don't have a rankig nsystem as i nthe UK or US)
other than that there are the universities of applied sciences, which are more.. British in teaching, evey also have compulsory placement years or semesters. a bit comparable to ex-polys i nthe UK i guess, they have however an excellent reputation with employers and are often even more compettitive to get into.