I would not suggest trying to repair your microwave, particularly given your apparent level of electronics knowledge. Yes, they sometimes can be repaired, depending on what is malfunctioning, and sometimes it may even be economical to do so. New microwaves are not too expensive these days, though.
A microwave oven, however, can be quite dangerous to work on; it's probably the most dangerous common appliance to repair electrically speaking. The power supply for the magnetron produces something like 3 kV at a substantial fraction of an ampere, which is plenty to cause electrocution by an ill-placed touch. Even when disconnected from power, it's possible that the capacitor could store a deadly charge. It usually has a bleeder resistor or other circuit to discharge it when disconnected from power, but of course with a broken oven there's no absolute guarantee that the bleeder is working properly.
This document has a lot of good information on microwave repairs (and doing them safely). One possible cause of the fuse blowing immediately is the door safety switch being broken or out of alignment or sufficiently clogged with crud to not work properly.