The branches have turned brown on my palm tree

What type of palm? Indoor or outdoor? Since we're left to guess, here's some information that may, or may not, help:
 

Once planted, a palm tree is easily maintained with just a little effort and some tender loving care.

The most important factor in a palm tree's health is soil.  Compacted, nutrient-deficient soils found in most urban environments do not contain the components necessary for a palm to truly thrive.  As steward to your trees, it is your responsibility to maintain healthy soil.  You can do that in two ways.

Adding Mycorrhizal Fungi

Mycorrhizal fungi coexist with plants in nature, colonizing the root systems.  In exchange for food, these fungi provide the plant with nutrients and moisture.  Effectively, they can extend the root area of a plant by up to 1,000% helping it survive under conditions of stress.  Soil in many urban areas and in most potted plants lacks this essential organism. By adding the correct mycorrhizal fungi to the soil, you are giving your trees a vital boost.
For more information about mycorrhizal fungi, click here.

Fertilizing

Palm trees require a large variety of nutrients to survive and because they thrive in sandy, well-drained soils, these nutrients tend to leach away quickly.  As a result, most common problems with palms are caused by a lack of nutrients or improper fertilization.  There are palm-specific fertilizers available that release their nutrients very slowly to provide consistent, targeted feeding. To find out what fertilizer you need for your palm, click here. 
 
Other Care Concerns

The most important consideration is to ensure that your palm receives sufficient water for healthy growth. In desert areas and in the absence of regular rainfall, periodic watering is essential. Slow drip or bubble type watering over a number of hours is better than a simple drenching with a hose. As for how often, this will depend on the climate, season and rainfall frequency. In many areas, twice a month during the summer decreasing to once every six weeks during the colder season should be enough.

As they grow, the older fronds of palm trees will turn brown, die and eventually fall off. For esthetic reasons, you may wish to speed the process along a little by pruning off the dead fronds. Use some caution when pruning a palm tree. Prune only the dead fronds and remember not to cut too close to the trunk. In the case of a large tree, this is a job that should be left to a tree maintenance specialist.

Finally, be careful when using lawn mowers and other gardening equipment around your palm tree. The bark is easily damaged and the resulting wounds are entry points for insects and disease.