Both the mechanics and cortexing skills run on broadly the same system. On a broken item, or a computer terminal phys-rep, there will be a set of problem cards that you need to go through. Each problem card can be solved by one or more solution cards. The solution cards are the mechanics or cortexing cards that you get when you buy the mechanics or cortexing skills.
You will need to go through each of the problem cards in turn, and the solution cards will tell you how long each one takes. You should spend this time roleplaying! You will need to have a mechanics kit phys-repped for mechanic’s problems, and some kind of cortexing rig or tools phys-repped for cortexing.
Your specialisations will come into play in that some problem cards will only be solvable by people with these specialisations, and they will give you extra options and time off the problems as appropriate – all the information will be on the problem card or given by a ref.