How to Clean Carpet

Rent a carpet cleaning machine. These are available at most grocery stores and super stores. Read over the instructions and pick the machine you feel is most appropriate for your situation. Purchase the cleaning solution required by the machine. Purchase a spot treatment for your carpet if needed as well.
Remove any furniture from the carpet that you want to clean.
Vacuum the carpet to remove any excess dirt from the surface. This should also expose any hidden stains.
Pre-treat carpet stains by spraying them with a carpet spot treatment before running the machine over the carpet. Allowing the stain remover to work in for several minutes should help loosen up the contents of the stain, enabling for easier removal.
Follow the directions on machine for adding cleaner and water. Plug in the machine and turn it on when it is on the carpet. Start using the machine by going in a back and forth motion over the carpet. Make sure to run the machine over the entire carpet, not just the soiled parts, otherwise you may see patches of cleaner carpet when it dries. You may want to run it multiple times over stained areas to ensure removal. You will likely have to stop and and empty out dirtied water and refill with clean water and cleaner several times before finishing the entire carpet. Make sure to note what the indicators for changing the water are by reading the instructions.
Stay out of the room until the carpet is completely dry. You may choose to turn on a fan to speed up the drying process.
Look over the carpet once it is dry and decide whether you want to re-run the machine. It can take more than one time to clean a carpet if it is really soiled. Re-run the machine or return it to the store if you are satisfied.