Palms require very little pruning. Basically the lower dead leaves or fronds are removed up no farther than the point where the remaining fronds are oriented horizontally or slightly lower. Some folks prune more away than this leaving only fronds pointing upward to some degree. This reduces the plant's leaf area excessively and is not a good practice. Specific frond removal practices depend on the type of palm and the area where it is grown (arid desert vs. humid southeast). Some palms drop fronds naturally in the humid south but may retain them longer in the arid west for example.
The following website from Florida Extension provides a lot of additional info on pruning palm trees:
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