Here is a video showing construction of an outdoor kiln.

Here is a print article describing open pit firing and building a brick kiln.

I’ve seen some indigenous potters who built what was basically a sheet metal box on short legs with a few small holes in the bottom. They’d put the piece inside and make a huge fire around it.

The type of kiln depends on the type of ware you want to produce.

I know a potter who has pit fired her work…nothing easier than building a big ass bonfire.

@Cruiser You just have to make sure that the fire doesn’t heat up to fast, or else it’ll likely crack the pieces.

A really simple and accessible way is to make a paper kiln. It requires a great deal of newspaper and patience… But, is really cheap and can be quite effective, if rather unpredictable. This site gives instructions and tells of some of the pitfalls.

Are you after something that will produce reliable results? As long as the core temperature of your kiln, whatever it is made of, reaches around 650⁰C (which is a bright orange/yellow glow) for at least 15 minutes then very simple earthenware pottery can be made really easily. A dustbin filled with straw can serve – similar to @incendiary_dan‘s note.

Have you thought about how you are going to regulate the temperature of the kiln? Without
proper temperature control, the results will be unpredictable.

You really need a kiln controller but since this is an outdoor kiln, I’m not sure how you are going to make that work.