To get started, set up the barrels. Start at the walk, walk to the barrel and keep him about 6 feet from the barrel with his nose turned slightly to it (this is called the pocket- you never want to get in the pocket as you are coming around the outside of the barrel, but you can get closer as you come around the barrel and head to the next one).
Let him get used to the sight of the barrels then move up to a trot. Trot with purpose to the first barrel. Stop at the pocket then walk around the barrel and trot to the second barrel. Stop at the pocket and walk around the barrel. Trot to the third barrel and stop at the pocket. Walk around the barrel. Go directly to the side of the arena - don't run for home.
Work on that over many sessions before moving up to a lope. Then lope to the first barrel. Stop and trot the pocket. Work on keeping your horses nose to the inside and an even six feet away from the outside of the barrel as you circle. Then come in close and lope to the second, trot around it, lope to the third, trot around it, and head to the side of the arena.
I had Scooby in training for four months and just got him back last month. The trainer patterned him doing the above steps, and now Scooby can lope the pattern cleanly. It will take another several months of attending barrel clinics and local shows before I will ask him for any speed. It is pretty deceptive how easy it looks, but the well-trained horses have had lots of time put on them with lots of slow work.
My trainer told me to only lope the pattern once for every ten times doing slow work, and keep him busy with other things ... so we take him on trails and cattle classes to avoid him getting sour.
Hope you have fun with it, I can't wait to get started!