There are three ways to fire clay pots if you don't have your own kiln, each of which would make a great homeschooling project!
We have been doing lots of homeschooling clay projects over the summer, and my children (inevitably!) asked if they could fire their own pots.
You cannot fire pottery clay in an oven because you cannot get high enough temperatures - but there are three options that would all make wonderful homeschooling projects for the more adventurous among you.
All of the above methods require low-firing clay (school pottery clay is fine).
When you first make a model, it is called 'greenware'. A first firing of this creates 'bisque' or 'biscuit-ware'. At this point the model is hard, but still porous so cannot be used with liquids. After glazing, a second firing will create a non-porous pot.
Only the first method of making a kiln will allow you to create glazed items.
Raku is a different method where you remove the pot from the kiln while it is red hot, then plunge into cold water or sawdust. This creates a lovely crackle effect on the glaze. I felt this was a step too far for a homeschooling project! But if you are adventurous enough to try, I would love to hear about it.
Your greenware must be totally dry before you put it in a kiln. This can take up to a week depending on the size of the piece, and the humidity. It is a good idea to pop the pot into an oven for a while to heat it up and make sure there is no more water left inside it, before firing. This should reduce the risk that the piece will crack.
Firing clay at home is very much trial and error. Be prepared for some disasters at first!
Smoke and Pit fired models benefit from being burnished first. Use the back of a spoon to rub the clay and make it smooth and shiny.
Normally a kiln is both heated up and allowed to cool slowly. Try not to allow sudden changes in temperature.
To really add to your homeschooling experience - there is a great chapter about making pots in Robinson Crusoe. There is a children's version of the chapter here.