Welcome Justhatchin
What Journey and Ridge said.
Ya see, the rootstock was started as a cutting or as an air layer, (which is a cutting, just not completely cut off until it has some roots. They wrap the half way sliced twig with special gauze with special potting soil in the gauze and tape it on.).
Well, when that rootstock gets growing, they cut it off a few inches up, a special kind of slice, and they take the twig from the good fruiting tree, (they like to use the weird word scion for this piece. Nobody knows why. Maybe somebody does.) Well, they slice that scion just right to fit on the just right slice they sliced on the rootstock, and they fit them together and tape them nicely, kind of like a spliced and set broken bone. Even kind of looks like a set broken bone's x rays.
Hopefully all that grows out of the rootstock are roots down in the ground. Hopefully the buds on the scion swell and grow.
Now, those buds on that scion, they are not affected in their chromosomes or genes by the rootstock, really not at all.
So that scion becomes the whole top of the tree, and that graft is right down there at the ground.
{{{just for those who know about the more complicated grafts, let's kinda leave that stuff out for now.}}}
Well, that top part of the tree is the part you want to take a cutting off of. Cuttings are fun, and as you might know or imagine, there are lots of ways to do them. Let's start with the cuttings that might be taken in January off a Pear tree. I'm going to presume you're in the northern hemisphere. A January cutting will be dormant. Most folks who aren't sure how a particular tree or shrub is for taking, would make a bunch of different size and lengths of cuttings, and stick some in a nice garden area, some in the house in a glass of water, and some into maybe gallon nursery pots with clean potting soil. Cuttings almost all "take" better when they have bottom heat. Wal Mart has nursery heating pads, 17 watts for something like 30 bucks.
Now, Smart Red is smart, and I trust what she says! Sounds like Pears have to be air layered. It's a half way measure that lets the tree help the twig to make it, to survive, while the cut sliced at an angle...only part way through!...with usually a toothpick or something in the slice to keep it open, is given a gauze wrapping with potting soil or garden moss or a good mix stuffed into it. I kinda think that'll take a coordinated assistant! And then, the grafting tape, which is like extra soft electrical tape, holds the gauze on.
Another kind of cutting takes place a few weeks to a couple months after the buds open. Spring softwood cuttings. That's the new growth. Soft, greenish stems, new pretty leaves and all. Take a bunch of those, a bunch of different lengths, and put those into pots. You can put like 5 into a gallon pot. First remove the bottom leaves, and yep, use scissors to cut the far half of each leaf off. Yup. Once stuck in the pots, carefully, real carefully with your coordinated assistant, put some clear plastic around those pots, with some air holes. You want to give them bottom heat, so that nursery heat pad is important.
Have a spray bottle handy with clean water, hopefully no chlorine in it, to give them a spray, and slowly remove that plastic each day, increasing how many times you spray them each day. You could add a smidgen microdose of fish emulsion to the spray water.