That is Wisteria, Hygrophila difformis. I would stick the cut ends of each stem in the substrate to get the plant growing. Plant it where it will have direct overhead light (i.e., not in any shade), the stems no closer together than 3 inches. This is a fast growing plant and needs lots of nutrients so dose Flourish comprehensive twice weekly.
It will once established readily grow up to the surface. You can then let it grow along the surface although the lower leaves on the stems will usually die off. Or you can cut the stems when you have a nice growing tip and let them float. Roots will appear from all the nodes along the stem. With the stems in the substrate, quite a large mass of roots will grow from the planted end of the stem, with fewer along the stem.