The Medicine skill can be a bit of a difficult one to use in-game. While it sounds good in theory, most games have a method of supernatural healing - especially in the various supernatural World of Darkness genres. This means that unless Medicine is a skill associated with that power, there's not a whole lot you can do with it at first blush. The first aid rules are essential in a game that uses extra mechanics like the Bleeding Out rules (if they take two lethal they start taking an extra bashing every so often to depict blood loss) but otherwise it just doesn't do much until they've filled up with lethal damage and are tracking into aggravated (basically, dying).
Possible specialties could include: Specialties: diseases, surgery, emergency care, pathology, pediatrics, pharmaceuticals, poisons, medical technology, dentistry, paediatrics, triage, autopsy, surgery, anesthesiology, dentistry, make-shift tools.
So what else can you do with it?
Diagnose an illness (Intelligence + Medicine)
Learn all of the patient's symptoms (Manipulation + Medicine)
Determine if the symptoms / injuries are due to natural causes (Wits + Medicine) and thus potentially identifying where the supernatural departs from the natural
Analyse an injury for its causes (Intelligence + Medicine)
Conduct first aid (Wits + Medicine)
Fake being a medical officer (Presence + Medicine)
Conduct surgery* (Dexterity + Medicine; sometimes Stamina + Medicine)
Conduct surgery without appropriate equipment* (Wits + Medicine first to determine appropriate replacement equipment to drop the penalty by 1 equipment penalty per success down to a minimum of -2 from -5)
Correctly pump someone's stomach of drugs / poisons (Intelligence + Medicine)
Perform a tracheotomy (Composure + Medicine)
Caring for someone who's injured (Manipulation + Medicine)
Appraise an injury in the middle of a firefight (Wits + Medicine to determine health levels in damage if using the Hidden Health extra mechanic from Armory Reloaded)
Prescribe appropriate medication for a medical issue (Intelligence + Medicine)
Ensure you stay healthy by paying attention to your fitness levels and good food to justify a physical attribute spend (Resolve + Medicine)
Defend against infection (Wits + Medicine)
Cope with a particularly horrific injury (Composure + Medicine OR Tolerance for Biology, etc.)
Conduct an autopsy (Composure + Medicine OR Tolerance for Biology, etc. just to stomach it; Intelligence + Medicine to conduct it)
Know the limits of the human body to check whether something should be possible (Intelligence + Medicine)
Trace a disease back to Patient Zero (Intelligence + Medicine with appropriate equipment)
Identify a poison by its symptoms (Intelligence + Medicine)
Recognise medications and their purposes (Intelligence + Medicine)
Understand basic human and animal anatomy (Intelligence + Medicine)
Knowledge of medical techniques and treatment (Intelligence + Medicine)
*NB: Surgery doesn't just indicate providing life saving treatment following health level loss but can also be used to remove failing organs, parasites, or implants.
You can find the core article with all of the other likely links over here.