I recently taught a class on how to make miniatures.  These are notes from the class hand-out. 
Below are a few things you need to do, and some things to consider.

What Type Of Clay Should I Use?
What Tools Do I Need?
How Do I Throw A Miniature?
How Should I Fire My Miniature?
How Do I Glaze My Miniature?
Important Hints
Pictures of students making miniatures

Any type of clay that does not contain any grog, or that has very fine grog, such as Porcelain or Porcelain-like clays will work. My favorite is a translucent porcelain called Glacia. 

What Tools Do I Need?

Since the pottery will be of very small scale, traditional hand-throwing techniques will be difficult. The following types of tools are in my tool box:

• small and very small brushes (make-up brushes work well)
• hat pins with a round bead/"pearl" at the end
• razor blades (I like the ones that have one side covered by a little metal plate, so you can hold it - available at drafting supply places)
• a very small torn-off piece from a bigger sponge or an eye-shadow applicator sponge
• jewelry tongs or long tweezers
• heat gun (also known as a paint-stripping gun)

The basic throwing principles apply to throwing miniatures, with some modifications. I will attempt to describe the steps below:

1. Take a larger (4lb or so) piece of clay and center it using traditional wheel-throwing centering techniques, concentrating on centering a small pointed cone on top of your clay. A fast to medium wheel speed is appropriate while opening, going to a medium speed after that.
2. Using the tail end of a paintbrush (as you would your finger if it were very skinny), open a hole of desired depth (about ½ inch)
3. Using the same tool, finish opening the clay out toward you to a sufficiently wide bottom, as you would open a regular size piece of clay, careful not to open it beyond the size of your original base.
4. To pull the cylinder wall up, apply pressure with the brush's stick from the inside of the wall (holding the brush vertical) and AT THE SAME TIME apply inward pressure from the outside with your fingertip, or with the top side of your nail (if you have long nails).
5. Shape your cylinder with your hat-pin, brush tail or hairs, sponge, or wooden tools to the desired shape
6. With the wheel spinning slowly, dry the finished piece to a leather-hard stage with the heat gun before removing it from the hump (it dries very fast). This makes it possible for you to pick up the piece by hand, attach handles, carve, or apply slip to the piece if desired. 
7. Trim off or push down some of the clay around the base of your piece before you remove it from the hump of clay. This will make the final trimming work easier.  
8. While the wheel is spinning slowly, with your foot on the pedal, use the razor blade to slowly cut away the bottom of the piece from the hump. WARNING - you will very likely cut too close to the foot of your piece and end up without a bottom, so take a good look at where your piece bottom is before cutting. No need to panic, you can always "fix" the pot by adding a bottom to it.

You can fire miniatures just as you would any larger piece of pottery.  I have successfully tried different firing techniques. My favorites are gas high fire and wood fire. 

I like using underglazes for hand-painted designs with a high-fire clear glaze on top, because I like  the translucency I get from the high-fire porcelains. 

How Do I Glaze My Miniature?

Glazing techniques are exactly the same as with full-size pottery. You bisque the miniature, apply any under-glazes or stains you want, and then dunk you piece in the glaze. In the case of miniatures, you can use long tweezers or jewelry tongs to hold the piece, so as not to make big finger marks on the miniatures when you dunk them in the glaze. Don't forget to wipe the excess glaze off the bottom

Important Hints:

Make a small dish to put your miniatures in as they travel from kiln to kiln and during the firings. The dish can be about 4 or 5 inches in diameter, and about 1 or 2 inches tall, bisqued, unglazed. It can be re-fired several times before you need a new one, even in the high-fire. Make sure that the inside of the bottom is flat, so the miniatures can sit in it without falling over as they are moved from the shelf to the kiln to be fired.

Take a break!

Not discussed here in great detail are non-high-fire firing techniques, such as Raku, Sawdust, and Pit firings. I have also used these methods to fire a few miniatures (not shown here), but have been unable to get satisfactory results thus far.

The Raku firing has worked somewhat (miniatures cool too fast), but the Sawdust and Pit firings have resulted in smoky, flat clay surfaces on my miniatures, which I did not find appealing. I have to spend more time burnishing the miniatures before trying these firing methods again.

I have also fired miniatures in a Wood Fire with great results. I recommend this firing techniques, if you can find someone that has a wood fire kiln. Be careful how you place your miniatures in the wood fire kiln, preparing for the possibility of finding your miniatures in the piles of ash in the kiln, or of your miniatures getting blown away, stuck to another pot, or stuck to the wadding.

Below are pictures of students making miniatures.