Alliance Trauma

First your character must be atleast level 35.
You must have your First Aid skill at 225.

Go to Ironforge.
Find the First Aid Trainer Nissa; she is in a shop right across from the gryphon landing in the great forge area.
Get the quest from her to go to Theramore and visit Dr Gustov.
Travel to Theramore; likely to the Wetlands and then to Theramore by ship.
Once in Theramore go to the keep; northwest portion of the city if I recall; once you come out of the docks take the pathway to the right; follow it to the warrior training area; then go right to get to the entrance.
Once into the keep; go right, then left, he is in the room in the back right corner of the keep.
Go to Dr Gustov and get the quest.

Key requirement is to save 15 injured all the while you will have injured dying - just cant let more than 6 die.

Now here are the tricks:
- Press the "v" key. This will show a title and status bar over all the injured soldiers. This makes it easy to see which soldiers are critical, badly or just injured.
- Step forward through the Dr so you have your character's back to the doctor; from this position you will be able to select and heal the patients without moving around.
- Use the bandages the Dr gives you.

Now at first I was confused and wasted alot of time looking for critically injured soldiers - initially there won't be any - only badly injured and injured soldiers. Just work on the Badly injured first.
- Now select a soldier and heal him with the bandages - good idea to put the bandages on a hot key spot just for the quest. The healing takes about 5 seconds for each patient; so it is slow.
- Use the time while you are healing wisely. Use it to look around for other patients. Find the Critically and Badly injured soldiers if there are any. While you are healing one soldier you can select your next patient. Once you finish healing one you should have the next one selected and this allows you to press your hot key and imediately start healing the next soldier. Believe me - every little bit of time you can take advantage of will help.

Good luck!

You must have 225 First Aid to get this quest and be at least level 35.

I recommend putting the triage bandages on a hotkey or an action bar. Your priority should be to first bandage critical, then badly injured, and then injured.

The reward will be Artisan First Aid. If you want, bring along mageweave and runecloth to get your skill up to 300 while there.
240 - he gives you heavy mageweave bandages
260 - runecloth bandages
290 - heavy runecloth bandagse

The line "Doctor <name>, I presume" is likely a reference to the famous quote, "Doctor Livingstone, I presume."