In order to turn your crawl space into a small basement, you will need to measure your crawl space and approximate the measurement you would like your basement to become. Next, approximate how large of a basement you plan to make. If your crawl space is approximately a good enough amount of space for a small basement, then you can start digging.
Using a shovel, dig into the crawlspace one wheelbarrow at a time, to get the depth and width you want. When you hit a support post, dig around it until you can get to the depth you want.
Pour a concrete footing four inches deeper than what you plan the depth of your floor to be. This concrete footing needs to be three feet square by three feet deep. Replace your original post with a longer one, preferably a steel post shore that is adjustable.
Once you get the center shored up, work your way to each outside wall. You will need a bit of creativity for this. You can dig as close as possible to the foundation that exists on all four sides, then pour a thick edge basement floor. On the thickened edge, construct a concrete or retaining masonry wall up to the height of the existing footing's top. This will keep dirt from caving in from beneath the foundation.
You can tie the old foundation to the new foundation with a poured cap beam and a re-bar. Essentially you will end up with a basement wall with a step in it or a constructed shelf all the way around.
The objective of all these processes is designed to bridge or fill the cracks in the foundation, which could possibly develop at a later date. These processes need to be used in conjunction with an excellent gravel back fill system and drain tile. Ordinary asphalt coatings are not waterproof. These will not bridge a crack in your foundation, putting your new basement's durability at risk.
Next you will need to waterproof your new basement. This process involves spraying a can of modified asphalt, which contains extremely flexible compounds. Special panels containing a clay that expands, or an expanding clay, can also be used.