Amos, we need to know where you are. Transplanting in Texas is ideally done in the fall so the roots can get established without fighting our summer heat. In the north, transplanting is done in spring, so the roots get established before the cold/freeze sets in.
Basic rules of transplanting--dig a big hole before digging out the plant; dig as much of the root ball with soil attached as possible; water thoroughly at planting time and then daily for about 10 days if it doesn't rain a 1/2" or more; and shade the plant if possible for the first two or three days.
I can't identify the shrub or tree from the photos, but someone more knowledgeable will likely be able to tell you what they are.