It's a fairly complicated process. Describing it would require a much longer answer than this site can accommodate.

You should get a lawyer to represent you if at all possible, and you should do so ASAP because you have a limited amount of time in which to act.

But before you decide to fight this, do think about what the agency told you. If you still have a risk of seizures then it really is dangerous to let you drive, even if those seizures might occur very seldom. You would be a threat not only to your own safety but to the safety of others.

Actually, a summary of the process is pretty simple to describe and theoretically you could do it in pro per, but I agree with Mr. Hoffman that it would not be a good idea, and also that you need to think about the reason the DMV did what it did.

As for what a writ of mandate is, in this context as opposed to taking a writ from a trial court action to the court of appeals, it is simply the inverse of an injunction. Under appropriate circumstances you can file an action against another party asking that the court issue an order that the other party stop or not do something. That is an injunction. A writ of mandate proceeding is a civil court case in which you ask that the other party, usually a government agency but not always, be ordered TO do something. Instead of enjoining them from doing something they are mandated to do it. In this case issue you a license. Where it gets complicated is proving your case, and establishing that as a matter of law the facts you prove entitle you to have a license issued. That proof of facts and law is not something I recommend you take on in pro per.

If this matter needs to be resolved, then contact me directly.