You do one side, then plane it flush. The next side overlaps the first edge. You plane that flush.
Some are built by doing the veneer first, then when cut at a miter, the veneer is also a miter. More common on production boxes. Has to be dead on.
Don't expect to get it right on your first try. Build test boxes. ( small with cheap veneer)
In other words, you do it just like you get to Carnegie Hall: Practice man, practice.