I have a square box 30" long by 10" high. I want to add molding around the box. I have a miter saw
The cuts 45 degree angles. But do I cut the pieces exactly 30" and 10" each. Both ends would be at a 45
Will they join correctly like a picture frame, or will there be gaps where they come together?

How do I cut the molding?

I would draw it out. If they are true 45's, their should be no gap.
1 Mitered cut will have the corner for another side, as you will be left with 2 45's?

First a square cannot have sides 30" by 10". That would be a rectangle.

Suggest that you first set the saw to 45 degree angle by cutting test material. That test material should be wider than the molding you will be using. The wider the material the more any error in the joint will show up. In other words if you are using 1" wide molding use 2 or 3" wide test material to set the angle of the saw. Cut four pieces and put them together to check angles.

It is just as important to have the parallel sides of equal length as it is to have the correct angle of cut. Set up stop blocks on you saw to make the lengths the same rather than rely on measuring and marking.

Finely, precut all the pieces. Cut one end of all the pieces. That is to say cut the left end of all the pieces at 45 degrees. Then rather than changing you saw settings, move the material to the other side and cut the other end. That way any error in the first cut will be off set by the same error in the opposite direction in second cut.

When cutting to final length, set the stop block a little long then sneak up on the final length.

Don't be easily discouraged. Cutting four perfectly mitered corners is not easy. The wider the molding the more difficult it is.

The box is a air conditioner.Being irregular in size it is a rectangle rather than a square.
The molding is 2". I did cut a prototype of a wider material in a preliminary test. Seems okay.. Affixing the molding to the stucco. I am using construction adhesive. Hope it holds.

Oh, thought you were building a jewelry box. If the stucco is firm the construction adhesive will hold with out problem. A cut nail in each piece to hold it until the adhesive cures won't hurt.