This is relatively simple. If you meet the HP requirement (unsure what it is at the current time) simply walk up to your faction leader and say:

You say, "I want to become a Soldier."

Your faction leader will then order you to kill faction soldiers (the NPCs that defend the flagpoles) belonging to opposing factions.

Kill the first soldier, and then return to your leige. Say something and they will give you information on the other soldier you will have to kill. Do this, return, and they will make you a soldier.