There are many different styles of pizza ovens. You can build a pizza oven out of bricks, make a barrel pizza oven, barrel brick pizza oven or an insulating dome pizza oven. You can choose to make any style you want depending on your preference and budget.
To make an easy DIY pizza oven that is transportable you will need: clay bricks, a base for your brick oven such as a cement board and an angle iron. This is pretty easy to make as you can pull it apart as soon as you are finished with it. It is also inexpensive so you don't have to worry about buying expensive material to make your very own DIY Pizza oven.