How can palm trees grow in the sand by the salty ocean water?

The vast majority of them can't. The one that can is the coconut palm - you can find out how IT manages at Botany: How are coconut trees able to produce potable coconut water within the coconut if they're located on a (saltwater) ocean island? read more

Coconut palm, sea grape, pine oak, white ash,red cedar and the saw palmetto are all highly salt tolerant trees. No beach scene is complete without a coconut tree and these are excellent choices for planting near the sea, as are true date palms. read more

Coconut palms can withstand plenty of environmental factors, including low or high pH, salty spray, slopes, insects, excessive heat and even poor soil. But when watering a coconut palm tree yourself, don't use water exceeding a salinity level of .6 percent. read more

Saw palmetto (Serenoa repens): One of the types of palm trees that tolerate salt very well. Saw palmetto reaches a height of 10-20 feet. Date palm trees (Phoenix dactylifera) are taller palm trees (50 feet) that are cold-hardy to 18 degrees Fahrenheit. The University of Florida Extension lists date palm trees as moderately salt-tolerant. read more