How do you become an instructor?
Another way to ask this question might be "What privileges do I need to instruct?"
In aviation, all flying privileges are granted through either certificates or ratings. Certificates are large classes of "licenses" that grant some kind of operating authority to the holder of that certificate. "Ratings" are add on "special abilities" if you will that permit the holder to operate special aircraft, under different flight rules, etc.
Here is a breakdown of all the certificates involved with instruction in the order that most folks use to get there.
Private Pilot certificate - This is the very first step. Anyone who wishes to do any kind of instruction starts here. This lets you fly day or night in visual conditions ("VFR" or Visual Flight Rules) most anywhere in the US and in some other countries (with some extra paperwork). You cannot be paid to fly in any way with a Private Pilot certificate. Most people start with a Private Pilot certificate for "Airplane Single Engine Land" or ASEL, meaning limited to airplanes with only one engine, and land airplanes (as opposed to seaplanes). Think of the "single engine land" part of this as a "rating". So you have a Private Pilot certificate with an airplane single engine land rating.
Instrument rating - This is a rating that adds instrument privileges to the private pilot's bag of tricks. Instrument privileges mean the pilot can fly under IFR (instrument flight rules) which allows flying in limited visibility and inclement weather, within reason.
Commercial Pilot certificate - When you become a commercial pilot, you surrender your private pilot certificate. You can now be paid to fly as a pilot for an approved operator, be paid for aerial photography, banner towing, cropdusting, etc. You cannot carry passengers for hire unless you are working for an approved operator. Should you choose, even though you have a commercial certificate, you can operate the aircraft using only private privileges. So you do not lose your private pilot certificate, it just becomes implied rather than explicit that you still have private privileges when you have a commercial certificate.
Certified Flight Instructor certificate - "CFI" - This is a seperate certificate that gives you teaching privileges in an airplane. When you combine this certificate with a commercial pilot certificate, you can act as a CFI, or Certified Flight Instructor. Acting as a CFI requires that all currency obligations of the commercial and the CFI certificate be met. The CFI certificate lets you teach, and the commercial lets you get paid for it. You cannot teach for free with a private pilot certificate + CFI certificate because a commercial certificate is a required prerequisite in order to take the CFI test, or checkride.
Multi Engine - This is another rating that lets you fly aircraft with two or more engines. If you add on this rating to your existing certificate, the normal way is to add it at the same certificate level of your existing certificate. In otherwords, if you hold a commercial ASEL certificate and get a multi, you'll take the commerical-multi checkride. When done, you'd have a Commercial certificate with single and multi-engine privileges. Airplane Multi-Engine Land (AMEL) is the most common type of multi. Note that it is possible to have a commerical-ASEL and have only a private-AMEL, but most folks don't do this. Also note you could have an instrument rating on ASEL but not AMEL, or vice-versa. It is possible, and common, to get a Commercial+Multi+Instrument checkride done all at once without taking individual tests for each little rating for each certificate type.
Certified Flight Instrument Instructor - "CFII" - This rating allows you to teach the instrument rating to students. This is a rating that is added to your CFI certificate. Note that you can actually get the CFII without the CFI, but this is a very illogical step and would allow you to ONLY teach instrument tasks and not allowing you to teach instrument emergencies, landings, etc. Additionally, if you have a CFI+CFII+commercial ASEL+commercial AMEL, you can teach instruments and everything else in a single and teach ONLY instruments in a AMEL airplane if and only if the student already is multi-rated. This is pretty close to totally pointless, since the entire meat of a multi+instrument rating is how to handle engine-out emergencies. You cannot teach this unless you have a MEI as well (see the next item).
Multi-Engine Instructor - "MEI" - This allows you to teach multi engine operations. An MEI by itself allows you to teach students how to fly multi engine aircraft. An MEI + CFII allows you to teach for an instrument rating in a multi engine airplane. Think of an MEI as equivelant to a CFI, except for multi-engine aircraft.