A tummy tuck removes the stock cross member and t-case skid and replaces them with a higher, stronger t-case skid. This raises the trans and t-case which is why a body lift can be necessary.
You gain a great deal of clearance where it is needed badly. With the OEM t-case skid being right between the tires, when going over large obstacles, that's where you have a tendency to hit. A tummy tuck skid is generally much stronger and smoother as well so you have less of a tendency to catch on it and the strength to slide over without damage other than scrapes.
The procedure for installation is to support the t-case, remove old cross-member and skid, install new tummy tuck skid (purchased form Jeep Medic, nTH, 33eng). It really is that simple. You can also add an engine skid as that will give you one smooth surface running along most the belly of the heep between the axles.