You need a small saw, whatever trees you're grafting, and something to bind them tightly.
Your trees can't be too big. You also need the trees to have either the same diameter trunk or the top tree can be a little smaller. It's really a judgement call. The younger the tree the better, because they're exploding into new growth instead of just maintaining. You cut the trees in half. Cut several inches down the middle out of the two sections you wish to bind together. Then cut horizontally on opposite sides for the top and the bottom. This will form two interlocking 'L' shaped. Put them together and bind them as tightly as you possible can. It will cause the two halves to fuse together.
You can use duct tape or buy special tape just for this purpose. Leave it on until you see it starting to cut into the tree. This may be a couple of years. You also need to make sure you hose the top tree down frequently to give it moisture till it starts growing into the other plant and tapping it's resources.
I don't know what base would be compatible with an avacado tree. Unless this is a fun project, I'd just buy one. Nurseries loose a lot of plants and only sell the ones that are strong and make it. They can afford the failures. It may get expensive for you.