Healing:
Within the "golden hour" after combat, anyone with a Healing skill (including the wounded PC) can try to remove the wound. A success removes one wound, a raise removes 2 wounds. Each attempt is 10 minutes (so 6 attempts are allowed). A couple of notes:
1 - Wound penalties of both the healer and the patient apply. So if both have a wound, the healing check is at -2. If the healer is healing himself, then count his wounds twice (once as healer, once as patient)
2 - If the result is 1 or less, then the attempt CAUSES another wound (oops). A hero that is already Incapacitated must make another Vigor check. Incapacitated must be dealt with before the wounds can be fixed, which takes up time
3. Characters that became Incapacitated (but not dead

) moves to Shaken with 3 wounds with the heal check. Then the wounds can be treated
4. If all the wounds are not removed in the Golden Hour, only natural healing or Greater Healing power removes them.
Natural Healing
Every 5 days make a Vigor check. Success removes 1 wound, 2 on a raise. A critical failure (1,1) adds a wound. Since you are running Deadlands, there are no bonuses to this check, but there are potential penalties
1. The normal wound penalty
2. -2 rough travelling (ie, you are not getting better in the back of a wagon)
3. -2 No medical attention (in modern/future settings you get a bonus from medical attention.)
4. -2 Poor environmental conditions (continual exposure to cold, rain)
The injury table only comes into play from Incapacitation. The results of when you become incapacitated dictate how long the injure lasts (end of encounter [raise], until the wounds are gone [success] or permanent [failed, but did not die])
Hope that helps.