Measure the length of each wall section at the base of the vault, and record the measurements. For crown moulding, measure the angle between the wall and the rear of the top edge of the moulding and the "drop" of the moulding or the distance along the vertical wall between the top and bottom interior edges of the moulding.
Note how two wall sections join together, at an interior angle or an exterior angle. Record this information to determine how the end of each moulding piece should be cut.
Cut the first piece of moulding. Test fit it in the location, and make any adjustments, as necessary. For crown moulding, use your angle and drop measurements to cut the mounting piece that will fill the angle between the vertical wall and the moulding. Nail up the mounting piece with a few finishing nails, using the level to keep it straight. Then, test fit the first cut crown moulding piece. Repeat this process for remaining trim pieces.