Paul,
1. Purchase the
Grafter's Handbook by R.J. Garner. Look up chip budding, t-budding, and topworking. I have personally had more luck with chip budding. I suggest doing it in July (the test of readiness is whether or not the cambium on the rootstock slips free of the wood). Before and after you graft, make sure the tree has
enough water. Drought stress will prevent the cambium from slipping or cause the graft to fail.
2. For budding you can get budwood from anyone you know who has an apricot (remember Puget Gold if you want to avoid brown rot in this climate). I'd get 15 to 20 sticks to be safe. Dormancy is only an issue for spring grafting where you harvest the scionwood during the winter. I would just make plans to get the budwood the same day you graft it. You will want to collect one year old wood (not the stuff that has just grown this spring). Put the buds onto younger sticks as well (think pencil diameter). Budding onto younger wood is a lot easier than onto thick trunks with old, gnarly bark. Check out the topworking pictures in the Grafter's Handbook to see what your finished product
should look like.
3. Don't get discouraged if your buds fail! Practice really does make perfect when it comes to grafting. Let the rootstock re-sprout from any branches with failed grafts and you can try your hand at whip-and-tongue, cleft, or bark grafts next spring or you can re-bud those branches next summer.
4. Make sure you maintain those buds! By this fall you should unwrap whatever you use to hold moisture in the bud (we use old chunks of plastic bags) and you should know which buds are likely takes and which have failed (based on whether they are dessicated, shriveled pieces of rotting wood or living, green buds). Keep on top of removing suckers coming up from the base.
Good luck!