I am too far away to get there in person but willing to try here. What type of grafting were you trying? Why don't you describe your process in detail and lets see if any problem pops out immediately. So when did you graft them, what type of grafts, how long were the scions, how did you seal/wrap the grafts, was the scionwood tight budded dormant, did you make sure the (green) cambium layers aligned? There are probably many other questions but these are a good start. I have taught myself to graft and while not a pro I have had some success.

Greenthumb

My first graft attempts were unsuccessful too. I was using too large of a piece of scion wood, using bad tools, and not sealing properly. Now I have very high success on apples and pears (which are pretty forgiving).

I'm assuming you are topworking existing trees. I'd suggest you use whip and tongue grafts with scion that matches a side branch on your existing tree. Cut the rest of the branch off beyond the new graft so the tree's energy goes to your new graft instead of the tip growth on the old branch.

I use a utility knife with retractable blade to make my cuts. The retractable type is very handy for opening and closing with your thumb and sticking in your pocket while you are grafting. You need to keep a straight, sharp blade in the knife. If your blade isn't sharp you will tear or bruise the bark and cambium layer and the graft won't take very well. Either replace the blade or hone it on a stone. If the blade isn't nice and straight your cuts will be curved and it makes it hard to mate the scion with the base stock.

When mating the scion to the base stock, make sure at least one side of the cambium on the scion is matched perfectly with the cambium of the base stock before wrapping. I use 3/4" black RUBBER (not vinyl)electrical tape slit in half lengthwise (3/8" width x 2 - 3" long. It will stretch and seal very nicely) to wrap my grafts because I can get it at almost any hardware store. Some brands of tape will deteriorate in the sunlight and won't require removal by hand, some brands are more durable and will require slitting with a knife about two months after grafting to allow the branch to grow without girdling. After you have wrapped the graft (be sure to cover the entire union) cut the scion back to 2 or 3 buds. Any more than 2 or 3 buds will tax the liquid transfer ability of the new graft before it heals. I sometimes seal the cut end of the scion with wax from a toilet bowl wax ring ($1.50 for a new one at hardware stores and will last you forever).