Your plant was grown in filtered sun, so it may wilt or burn if given full sun or too much heat right away. So i recommend starting your plant with either filtered sun, or a few hours of morning or late afternoon sun. The easiest method is to transplant it into a small container (1-3 gallons), so you can move the plant around. Start with about 2-3 hours of morning sun, and increase by about an hour every 4-5 days. If afternoon temperatures get over about 85 degrees, try to give it some afternoon shade for the first month. After about 4-6 weeks, simply repot in the ground, or into a larger container (5+ gallons).
Repot gently to avoid damaging the roots.
Parrot's Beak has average fertilizing needs. Feed about every 2 months with a general-purpose fertilizer that contains micronutrients (I use this).
Try to keep the soil evenly moist of the time (not constantly soggy though). If you're unsure if the soil has the proper moisture in the root zone, use a moisture meter.
Parrot's Beak is supposed to withstand frosts down to 15 degrees F, however i don't have any experience with them in freezing weather, since it doesn't freeze here. I would protect the plants with a tarp if freezing weather is expected. Or just bring them indoors, if you're growing them in a pot. In very hot climates, they should probably have some afternoon shade, or at least shade the pot, to keep the roots cool.
Pruning isn't necessary for this plant, but you may remove any undesirable branches.
Bugs to watch out for - spider mites (tiny "dots" under the leaves), mealy bugs, caterpillars, and slugs/snails. Try using insecticidal soap before using stronger remedies, since some may harm the plant.
Enjoy your plant!
Strange Wonderful Things