Hi Laura,
to All Things Plants!
I agree with Dutchlady, your plant is a Hoya, probably
Wax Plant (Hoya carnosa)
https://en.wikipedia.org/wiki/...
Many Hoya's like the one in your photo have thick, succulent like leaves and require a well draining potting medium. You can add a lot of perlite to the soil to accomplish this or mix some orchid bark in with the soil. Hoya carnosa loves high humidity so placing the pot on a tray of wet pebbles or misting the plant every so often will help raise the humidity and keep it happy. If you use a tray with pebbles just remember to add a little water to the tray every so often.
You can propagate the plant by stem cuttings but if you cut those stems you may lose the possibility of blooms forming on the mother plant for a long while. If you do decide to cut the stems, don't bury them too deep but rather lay the stems on top of the soil and weigh them down with a small rock ... they will take root at each bump/node along the stem.
A site with great growing information for Hoyas and beautiful photos!:
http://vermonthoyascom.fatcow....
