How do you make a dovetail box?
And a more complex box here:
What is the best way to fix a base on a box?
It depends on the size of the box. A glued/nailed on bottom is perfectly strong enough for a lot of situations. In fact, many old toolboxes had bottoms that were glued and nailed in place so that they were easily replaceable when the time came to do so. They allowed the movement that was necessary in wider boards. You can see an example in our series on the Joiner’s Toolbox.
You can also make a mortise and tenon panel as shown in our Tool Cabinet series.
This is still glued and screwed in place, but the panel ensures that the grain direction of the bottom is in line with the sides.
The final option, is to plough a groove a little way up from the bottom on the inside of all four faces to fit a board or piece of plywood into. This is the method used in drawer making and can also be used in box making.