You may get different answers then mine, but the way I’ve done it is graft the dormant scion onto a loose rootstock, wrap the graft union with tape or something similar, wrap the whole thing with a damp paper towel and place in a tied up plastic bag.
I put the bag in a dark cool place and let it sit a few days, and maybe after a week or two, if the graft took, you should see new green buds peek out on the scion.
I let mine sit a few days to see how it progresses in the bag. After a week or so, I potted them up in a 3 gal pot with the appropriate potting soil, making sure the graft union is a few inches above the soil. After that, I just left it outside to grow, and watered it a bit when needed. If it’s hot out, you may need to set it in the shade at first and get acclimated to the weather, and then gradually let it get more sun. You could plant it in the ground probably the following fall where you want it. Some folks would transplant it to a garden spot in the spring and let it grow like any other veggie, and then move it that fall. Or even leave it there until the next spring and transplant it to its permanent location.
I did that with 3 apple grafts last year, and they’re in the cellar now because it’s too cold right now to plant them. I hope to plant them in the ground in March before they come out of dormancy.
Just my 2c, there are way more qualified folks on here who might do it differently.
If you’re not ready to use the rootstock immediately, some folks store them in pots with some moist peat moss or soil over the roots, and store in a cool dark place, or maybe heel them in by digging a hole for them outside, and laying just the roots in the hole and covering it back up with the soil.
What are you planning on grafting, apples, pears, peaches?