Around the Ring
Here are some photos of a good friend and myself taking our little girls through a UKC ring. In the ring the judge will tell you what to do but usually it starts out with the judge telling you to take them around the ring. Here we are going around the ring.
On the Table
After the initial go around the judge has you put your dog on the table (for certain breeds they eliminate the table)in order to completely go over your dog. When they do this they are checking for soundness of the dog's structure. They will either check the bite themselves or have you show it. After that they run their hands over the dog and check for muscle strength and general structure of the dog.
Down and Back
Here the judge has you take your dog off the table and move it for them. My dog is doing a 'down and back' here. There are several ways a judge can ask you to move your dog, down and back, triangle, reverse triangle are ways that the judge will ask you to take your dog through the ring.