HI Carol, I've never done this with a tulip tree but have great success with Rhododendrons and such.
There are two ways to do this and PLEASE believe me this is how I did it and had good results BUT, don't blame me if it has not worked.
1st way is called AIR Rooting, take a branch about as thick as a pencil or JUST slightly thicker.
12-18 inches down this branch, take a clean very sharp knife and just below a leaf bud, make a slanted cut (DONT CUT RIGHT THROUGH THE BRANCH) you just want a thin cut upwards to include the leaf axle.
Next take match stick or tooth pick and place this into the cut (ACROSS the cut).
This toothpick will hold the cut open, take a blob of cotton wool, and dab into rooting compound, and dust the cut and around the wound. (apparently there's a Chestnut compound new, to help rooting) but Please check this out before you use it.
Next you need to wrap a 12 inch long pocket a clear polythene and tie off the bottom by using twine, carefully fill the pouch with sterilized peat moss (garden store or florists) make sure the moss is damp to help keep the open wound cool but not soaking wet.cool . Pack this as tightly as possible as you dont want air to dry out the moss, dont force the pouch full as you need to have it firm but not damage the cut area or it will sever from the branch,
next, tie off the top of the clear pouch, leave this in place for a couple of seasons but after 1 year, check to see IF there are any small roots starting in the moss, it can take a couple of years or it can take one year, it all depends on nature, temp, condition of branch you choose etc.
The second way id exactly the same prep of the thin branch by cutting, holding the cut open ect, instead of making a pouch and filling with moss, you need to select a branch that can reach the ground, or large pot placed beside the tree and the selected branch can reach.
You scrape away some soil where the branch can reach, place the prepared cut on the branch into this small groove and cover with the soil that has had ground up leaf mould or good humus added to the soil. once the branch is in place under the soil, you need to peg this in place with thick wire pegs (MAKE yourself bu bending the wires, on top of this, add a large stone so the branch cant be moved around when it's windy. the part of the branch that will form the new tree, (growing end of branch) this needs to be tied to a cane or stick so it points upwards as in a growing tree, if you dont de that, the branch will lay on the soil and can rot or become damaged beyond what you would want to use as a tree / sapling.
After there has been enough roots formed, you need to cut the rooted part of the branch away from the parent and this is the same for both ways of rooting.
I know this sounds long and a lot of work but honestly it is not all you have to remember is to get everything you require ready do your not left running about with a cut branch ready to part company from the parent because you had to leave it hanging in the air. OH by the way, are you aware that tulip tree's dont flower for at least 12-15 years old. ?????
there is a simpler way by just cutting a stem off the tree and sticking it into the ground but with most slow growing tree's / shrubs, they are inclined to rot long before they take roots.
Very best of luck, lets know how it goes IF you go ahead.