Like most other skills in LotFP, First Aid starts at 1 out of 6, and can be increased by characters who can spend skill points. It has three different uses.
1. A successful First Aid check by a PC on another PC or sufficiently humanoid NPC can be used to restore their level in HP. A character can only benefit from this type of healing once per day (or once before needing to rest, which I think amounts to the same thing). One player can use this type of First Aid on multiple other characters more than once per day, but each character can only receive First Aid this way once per day from anybody at all.
If a character uses First Aid on themselves in this manner, they must do so with a penalty of 1 skill point. This means that a character with 1 point in First Aid cannot perform the skill on themselves, a character with 2 points in First Aid only has a 1 in 6 chance of it working on themselves, etc.
EDIT: I think this First Aid ability should take 1 turn, and should probably not be available in combat.
2. If a character is below 0 HP but not yet dead, a PC can make a First Aid check to restore the dying character to 0 HP, at which point they are unconscious but stabilized (i.e. not losing HP from blood loss). Before making the First Aid check, the player attempting to do so must spend 1d3 rounds attending to the dying character; other than moving to the character at the beginning of this process, the player making the First Aid check cannot take any other actions without causing the attempt to automatically fail. After the 1d4 rounds, the First Aid check is made, and if successful the target is healed to 0 HP.
3. If an injured character rests for a full day, another character can spend 1d8 hours attending to them with a successful use of First Aid in order to double the HP regained by the resting character that day. Failure means the 1d8 hours were wasted, and the resting person only regains HP as normal.
If an injured character wishes to use this skill on themselves to double their own healing during a full day of rest, they can only do so at a penalty of 3 skill points. This means that a character with less than 4 points in First Aid cannot use this ability on themselves.
A character can only benefit from this type of healing once per day.