Hi Raymond, (part 1)
I think the most important thing to remember is try to keep a big a root-ball as possible when digging out.
Obviously the smaller the tree/shrub the less the task will be and visa-versa.
Start by digging a trench out with a spade at a good distance from the stem, to determine how far the roots have radiated out from the trunk, keep digging down and eventually the root-ball should start to loosen.
Basicly there are 2 types of root's, Anchor roots and fiberous or feeder roots. Try not to knock off any soil thats clinging to the roots, as this will be a set-back to getting the tree successfully transplanted or not.
When you can safely lift out the tree, it's important to keep the root-ball well covered from drying winds, so keep it wrapped in some damp sacking or polythene to keep the moisture in.
Now you should have a good idea how big to dig the new planting hole, estimate this then add a bit more for good measure!
It should be planted at exactly at the same depth as it was before, so make sure you get it right by testing it before finally back-filling!
Once you're happy with the size of the hole etc, start forking the bottom and sides, this will help the roots to penetrate the soil rather than them going round and round in circles.
It's always a good idea, I think to add plenty of organic matter at this point, leaf-mould or general well rotted compost is fine, just mix it in with the soil to get a good friable texture.
Firm it in well as you go whenback filling to exclude any air pockets.