I cut these twigs off a local mulberry tree which bore what I thought was particularly good fruit last spring. In October I took lengths about 8" long and removed all the leaves from them, putting the down end in a glass of water filled about 1/2 way to the top of the twigs, and leaving this in a not very bright place. About 6 weeks later, when I checked to make sure the water had not all evaporated, I was delighted to see little leaves starting to form about 1/4 way from the top.
So I cut off the top and drilled holes in the bottom of a SmartWater bottle, filled it with hydroton clay "rocks" stuck the twigs into the rocks, then nested the bottle into a larger bottle 1/2 full of water. will add a picture of my contraption when they start growing roots and leafing out some more.
This was how I started a beautiful fig tree a couple years ago. Mulberry trees are rather messy, so I am not sure how good an idea it is to try to grown one indoors in water, but it promises to be a fun experiment.