I trained our cat Gizmo to do several tricks. I live in Boston, and she lives in Rochester, and I wanted to see if she remembered me. I followed a clicker training methodology: every time she performed the behavior I wanted, I made a clicking sound and gave her a treat. I started out with a simple behavior (such as walking through a hoop), and then gradually increased the complexity (e.g., raising the height of the hoop). I found that she would not learn if the behavior was too simple. If the hoop was too low on the ground, she would walk through it, but not realize that it was special. I had to raise it high enough that walking through it took effort, but not so high that she could walk underneath it. Once she had the idea that she should pass through the hoop, I gradually increased the height until she was leaping. She performs her tricks reliably even without reinforcement for many months.
It takes about three days to teach her a new trick, with three or four five-minute training sessions per day. Refinements, such as increasing the height of the hoop, take longer, but she was doing a recognizable jump after two or three days of training. I did three or four five-minute training sessions per day.