we did it as an A-level experiment for about 3 years.
First year no success then after that we did.
Clean sharp blades and we used micropore tape and Vaseline for the grease.
chose the graft that is a similar size to the host plant. This will help the tissues line up better.
the pupils tried just a bud as they do in roses, others short twigs cut at a slant to match the slanting cut on the host . If the materials were left exposed to the air for about 30 mins seemed to do better than immediate joining or those left for longer than 30 mins.
The best results came when they chose apple to apple etc rather than apple to pear or apple to plum.

be interesting to see how you get on.

As Sbg says, the whip graft is the easiest for beginners. Shield budding is fairly easy to learn, but it takes practice to get the necessary speed and accuracy. For tying materials, wide rubber bands--preferably natural--seem to work best. For sealants, I've found beeswax to work the best, though where I live, I have to remove it before the temperature goes over 105º F. Don't be discouraged by some failures: they even happen to the experts. :]