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Your plant looks like a variety of Epiphyllum cactus. In nature, they grow on other plants, but only use them as a support. They're great in hanging baskets because of their long, pendant shaped leaves. They are only hardy to about 50F, so if it's supposed to get colder than that, be sure to bring it in or at least cover it. Because of where you live, you frequently get nights like that during the winter. They are fairly inactive in the winter, but the growing/blooming season starts in late spring to early summer. It prefers partial shade to full sun. If you give it brighter sun in the spring, it should produce more flowers. Unless this plant is located where it gets the usual rain for your area, you'll need to water it. In the summer, keep its planting medium moist. Cut back some in the winter when it's not actively growing. Make sure whatever you have it potted in drains very quickly, to mimic its growing conditions in the wild.
To propagate them, cut them off at the base of one of the segments on the leaf. Store them in a cool, dry place for 10 days—do not plant right away. This resting time will allow a “callous” to form that will protect the leaf from rot as it is rooting. If you can, chose potting mix for epiphyllum cacti.: 3 parts potting soil mixed with one part of coarse non-organic material such as perlite. The non-organic material should be 1/8 to 1/2 inch (1/3 to 1 1/4 cm) in diameter. You can also add 1 to 1 1/2 tbsp. of orchid bark per pot.
The potting mix should always be damp, never wet. This will ensure healthy and faster growth. The best way to get the potting soil at the correct moistness BEFORE you plant the cuttings is to put the potting mix (as described above) into a bucket and add hot water—probably about a cup of water to two cups of soil. Allow it to sit for 5-10 minutes so the potting soil can soak up the moisture. Then reach in and take a handful, squeezing excess moisture from it—it should be as moist as a wrung out sponge. Fluff it up and place that in a plastic 4 inch pot with a hole in the base. Place the cuttings in the soil. Don’t water—allow the cutting to form roots. Too much water will cause rot. To test if the cutting is rooting properly, gently tug at it. If there is resistance, it is forming roots. If it pulls right out, it’s probably rotted. You can cut away that segment of the cutting, let it cure again for 10 days, and start over.
Here’s more information about growing your cactus: http://www.wikihow.com/Grow-Epiphyllum-Cactus