Hi!
If you haven't figured out how drafting works in Civ4 yet, then maybe I can help out a bit. If you did, then you could just ignore this message.
I have included a screenshot to go along with this. You will need the nationhood civic, which is available after researching Nationalism. When you go to the city screen, you'll see a "draft" button at the bottom of the screen, next to the map. In order to draft a unit, the city you selected has to be at a minimum population of 6. Also, your culture must be the dominant culture in the city.
When you draft a unit, you will lose population in that city and cause a certain amount of unhappiness for a few turns. However, you will receive a standard soldier unit that you can instantly use. Also, you can only draft three to five times per turn.