It's kinda late in the season for transplanting without shocking the tree. This is better if done in Feb. If it has a mature root system I would dig up as large of a root ball as possible. Go wide and deep.

They do transplant fairly easily from my experience. Agree with Chadec7a that it's best to do it in the late winter before they leaf out. You can get a head start by root pruning around the plant so it forms a tighter rootball and will transplant easier. Make a circle with a spade around the approximate size of the roots. Don't dig too deep or try to actually lift the plant out. Do this a few times this summer and fall to keep the roots growing with in that circle. By the time you go to transplant it, the rootball should be nice and compact and easier to move.

Crapes do very well by hard pruning because they only flower on new growth. You might benefit by hard pruning after you transplant, but I would research that first.

I transplanted one in March and it has never leafed out. So be prepared to possibly lose this years bloom's if you move it now. They are super strong and will come back, you may just have to wait a year.

I wouldn't hard prune a Crape. They are a four season tree: Their flowers are not their only attraction. Their fall color is gorgeous and their fresh spring foliage is so pretty. The part of year they are completely bare shows their beautiful form and bark. Hard pruning would make them look ugly in winter.

Palms and Crapes together are really beautiful together.

I had someone transplant a crape and now all the leaves and flowers are dead. The tree is still alive. Should I cut back all the dead areas (including the branches) so it loks like an early spring prune, or should I leave everything as it is and hope it comes back?

If there is green under the bark when you scratch it, it will come back next year. Right now I wouldn't prune it unless the branches are dead. Any unnecessary pruning will just cause more stress to the crape Myrtle.