Best way to join box sides?

The term you are looking for is “joinery”.

Fingerjoints can be done:

but the typical void-free form requires a fixture to hold stock vertically:

I’ve been working on this for a while, and have worked up a fairly straight-forward technique for doing it flat on the table:

see:

but it requires having a narrow V endmill.

If you are willing to have exposed endgrain, a similar technique is:

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