Treating Wounds Without Magic

The most basic thing a healer can do is help mitigate pain. Typically this is done with herbs and poultices, splints and bandages. A healer can roll Intelligence + Medicine or Intelligence + Hearth Wisdom to try to mitigate a subject’s pain. The difficulty is 5 + the subject’s wound penalty. Success means the subject halves their wound penalty (round up) for at least a day.
A healer can help expedite natural healing. For bashing damage, roll Intelligence + Medicine difficulty of the 5 + the subject’s wound penalty or Intelligence + Hearth Wisdom, difficulty of the 7 + the subject’s wound penalty. Success means the subjects healing time is halved.
Expediting healing for lethal damage is much harder. Roll Intelligence + Medicine, difficulty 6 + the subject’s wound penalty. Each success lowers the difficulty of the subject’s Stamina roll by -1 and reduces the base time to heal to the next level by 10% per success rolled. See Natural Healing Times for what the base time normally is.
A subject injured by lethal damage is exposed to the potential for losing additional health laws due to bleeding or infection. To stabilize such an individual, roll Intelligence + Medicine or Hearth Wisdom against a difficulty 3 + the subject’s wound penalty. A single success is all that is required to avoid further injury. If the subject is crippled or Incapacitated, stabilization efforts take at least an hour.
Note that a single dot of Healing magic can also stabilize a wound and prevent infection, but it won't expedite actual recovery. Thus, a lot of magical novice magical healers have to rely primarily on mostly non-magical healing means.
A healer with limited access to medicinal aids requiring improvisation needs to roll against a higher difficulty than what is stated. A healer in an exceptionally well-stocked hospital or temple apothecary can get a -1 difficulty break in her favor.