Besides knowing how to correctly transplant a tree or shrub you need to know when to do it and what you are dealing with. Is the tree/shrub going to be a nursery purchased tree/shrub that usually has been balled and wrapped in burlap or is the tree/shrub something you just want to move from one place to another and you have to dig it up yourself?
If you are digging up a tree/shrub and moving it then make sure you dig the new hole where it is going to first because the longer the tree/shrub is out of the ground the least chance it has of surviving. Also if you are digging up a tree/shrub to transplant try not to shake off a lot of root dirt or cut into the roots with your spade. Prior to digging measure out a 3 foot circumference from the trunk of the tree/shrub and that is where you start digging. Remember moving bigger tree/shrub means you are personally moving a lot of mass and this is where you may want to call in a professional.
Will this transplanted tree/shrub need lots of water? If so, do not plant it near one that does not.
Will this tree/shrub require a lot of sun or share? How big will this tree/shrub grow in width? You need to make sure that you know this so you do not have to move it again should it become to large for the area you plant it in.
Once you decide all this and your start to dig your new hole make sure you measure either the root ball of the nursery tree/shrub or the area of the tree/shrub roots you are digging up and then make the new hole twice the size of the root ball or the tree/shrub roots of the tree/shrub you are digging up.
Make the depth of your hole a little shallower and resist trying to soften the bottom of your hole with your shovel or spade thinking it will help your tree/shrub roots.
Now back to transplanting a tree/shrub should be the case because you will need to have a tarp handy to help with the project. Once you have loosened or dug up the perimeter you will be able to get your spade or shovel under the roots and pry them up. Then you will be able to lift or drag you tree/shrub unto the tarp which you will drag to your new location which is hopefully nearby. If not you may have to ball it up and move it to where you want it to be.
Now that you have the tree/shrub next to the new hole, either un-ball and unwrap it from its burlap or slid it from the tarp into the hole. Now straighten the tree/shrub and gently cover all the roots with the soil making sure you are tamping down all the time to remove air holes or air pockets, which when left, are the surest thing to make sure this tree/shrub shifts or does not survive. As you tamp make sure you water as you go for this also eliminates air pockets.
Next I like to make a berm of dirt around the perimeter of my tree/shrub or shrub that will act as a catch basin for water because from here on out until your tree/shrub has established a good foot or root hold it will need plenty of watering and do not depend on rain.
Next I like to put about 3 inches of good mulch around the tree in about a 3 foot diameter. However, I keep the mulch about 3 inches from the truck of the tree because rodents and other critters like to frolic in mulch near the tree trunk. Also my daughter-in-law's cats love to defecate in any newly turned over dirt that does not have mulch covering it.
We live in a very windy area so when we transplanted a whole orchard we had to make sure we rope staked our trees down with ropes and pegs from 3 different angles and we had to leave them on for about 4 years or all these fruit trees would really be tilting at a weird angle.
Because we have a lot of deer who love bark of new trees we had to wrap the trunks of the newly transplanted Cleveland and Bradford pear trees along our driveway and these wrapping were left on for about 4 years until we knew they were established enough to not be susceptible to the deer. This same thing was done to all the fruit trees in the orchard.
The best time for transplanting is late fall or early spring. Don't try it in the summer because it is usually too dry. I remember our late son Fred hauling down truckloads of water in big garbage cans for about 5 weeks when we planted trees along both sides of our 900 ft long driveway.
I have found that it takes about 2 hours to property plant or transplant a tree or shrub and that is something else to consider when you are doing a lot of trees or shrubs.
I found the best tool for digging is a good pointed shovel. You will also need a measuring tape, a long hose for watering or a good big bucket for hauling water. You will also need a good size tarp, some bags of mulch on hand and a pair of good pruners. Having some people to help you is a big asset also.
Once you are set up ahead of time and especially if you make it a family project you will get along fine.