For most people, attempting this is a very bad idea.
I have had some luck with simple things, and if you are willing to accept the risk of total disaster and have some experience already with working on small high precision things, you can try your hand.. There is a lot of information online. You will probably need to invest in some high quality tools.
One fairly simple thing if you have a stiff focus rack, is to take it apart, clean all the old and hardened grease off using paint thinner (or xylene if the stuff is really difficult) and regrease the rack. Only a tiny amount of grease is required. I use tri-flow synthetic grease, but almost anything could be used, even vaseline.Avoid touching optical surfaces. When it comes to cleaning lenses and prisms, the general byword is to do no harm. The worst thing to do is to grind scratches into the lens by rubbing dust and grit. Blow as much of this off as will move using canned air. Then a single wipe with a Kim-wipe or some such lint free towel, moistened with just water. Throw this away (along with the grit it has removed) after one wipe, and continue. Endless rubbing is foolish and almost guaranteed to cause damage. Wipe off any water to avoid water drops and you are done.
Cleaners with ammonia (like windex) can damage lens coatings. Any solvents beyond water can damage the glues used to cement lenses and should be used either not at all or sparingly and with good reason.
It is fairly common to find used microscopes for bargain prices with serious alignment problems. I have managed one such repair with infinite patience and lots of trial and error, along with a good measure of plain luck. Most such cases should simply be avoided.
Tom's Mineralogy Info / tom@mmto.org