Young Palms are a bit tender. They like to spend the first years of their lives in a shaded, protected spot. As they are easily transplanted, you might consider planting your Palm temporarily under some well establish shade trees to give it the best shot of growing happily with the plan of moving it later to its permanent home. Most Palms like full sun but they all tolerate some shade even as older specimens if you'd rather leave it where it is.
Once you have your Palm the planting is easy. Use good, rich soil amended with compost and organic matter and dig a planting hole only as deep as the root-ball and 1-2 feet wider. Center the Palm within the hole and back fill pressing the soil around firmly. If it is a big Palm, already a few years old or a transplant, staking might be necessary. Palms don't have much by way of roots to keep it firmly in place. Water it regularly and often until well established. Providing a bit of shade around the roots by way of a thick mulch wouldn't be bad either just to keep it from drying out.
Frequently spraying the Palm leaves with the hose is advisable for dislodging any wondering insects, cleaning off foliage and for providing humidity. After that you'll have nothing to do but admire your Palm. The only other maintenance they require and this is for some cultivars who may not shed their leaves cleanly, is to cut them off or trim the leaf base to keep the trunk looking neat.
If you live outside of the comfort zone of all Palms, which is very likely, you may like to have one indoors. To do this is quite easy. Cultivars more commonly available that take well to indoor living are Howea Forsterana (Paradise Palm), Rhapis Excelsa (Lady Palm), Chamaedorea Elegans ( Parlor Palm) and the dwarf Phoenix Roebelenii (Pygmy Date Palm). For temporary indoor Palms, those that will exceed ceiling heights eventually but still make nice indoor plants in the first few years, try the popular Washingtonia Filifera (California Fan Palm) and the very slow growing Chamaerops Humilis (Mediterranean Fan Palm).
Knowing all this it should be easy now for you to keep a Palm tree in your landscape or at least in the sunny "Florida" room in your home.