Start your plant in a pot about 50% wider than the pot it's currently in. Repot gently to avoid damaging the roots.
To avoid burning or wilting, start it in filtered sun and gradually move it into brighter light over a period of several weeks.
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. Don't let it dry out. If you're unsure if the soil has the proper moisture in the root zone, use a moisture meter.
Mature plants are reported to withstand a light frost, but i recommend protecting it from frost.
In very hot climates, they should probably have some afternoon shade, or at least shade the pot to keep the roots cool, perhaps by placing the pot inside a larger pot filled with soil.
Pruning isn't necessary for this plant, but you may remove any undesirable branches. Feel free to tie the branches upright if you don't want them to grow sideways.
Repot to a larger pot whenever the roots fill the bottom. An adult plant may be kept in a 5 gallon (20 liter) pot if occasionally pruned shorter.
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