Ask Mr. Smarty Plants

Mr. Smarty Plants needs a little more information before we can definitively diagnose your palm problem. Without knowing the type of palm, it is more challenging to offer advice about what is causing the browning of the leaves. Also whether the plant is growing indoors (which I assume) and not outdoors would also assist with the diagnosis.

In any event, if it is growing indoors there are several general causes of leaf browning that deal with the root health and the frequency and type of watering that could be the problem. Indoor palms are extremely sensitive to chemicals in the tap water and should be watered after the water sits for 24 hours. Browning of the leaves could also be caused by underwatering (also caused by the roots being pot bound), overwatering, root rot and fertilizer buildup.

http://www.extension.umn.edu/garden/yard-garden/houseplants/growing-palms-indoors/

The University of Minnesota Extension has an informative webpage on growing indoor palms. Here's what they say about brown leaves and watering for several palm types:

Though their light requirements may differ, all these palms have similar needs when it comes to water and fertilizer. In fact, dried brown leaf tips or leaf margins, two of the most common problems facing indoor palms, are related — directly or indirectly — to how they are watered and fertilized.

Keep palms relatively moist. In spring and summer, or when temperatures are warm and days are longer, water them as soon as their soil feels dry a little below the surface. Allow the soil to get slightly drier in winter.

It's important that potting soil drains well and containers you use have functioning drain holes. Water palms thoroughly, then spill or siphon off excess water that collects in the tray or saucer below the pot.

Fertilize lightly from late winter through early autumn, the time when houseplants are likely to grow most actively. A build-up of fertilizer salts in the soil results in those dreaded brown tips and edges, especially if you allow the soil to get too dry between waterings. If you're unsure about fertilizing, err on the side of too little rather than too much. You can always fertilize again, if necessary.

Finally, keep palm fronds clean. Spider mites are attracted to dusty foliage and can balloon into a serious problem, particularly in winter when relative humidity is low indoors.