Remove the brown slime stringy material (you can often siphon most of it out). Do this while the coral is still in the aquarium. Hold the siphon an inch or so away from the slime and start the siphon. Dump whatever you siphon out into a bucket. Do not reuse the water in that bucket. It is laden with elements and chemicals you do not want back in your tank, besides the slime that you removed and that you do not want in the tank either. Note that sometimes you need to siphon this off several times, hours apart or on consecutive days. Slime may reappear and needs to be removed.
Dip the affected area in water for about 3 to 4 minutes. You need to use saltwater and add iodine to the water to kill off the bacterial disease. How much iodine you add depends on the strength of the product you use. Some brands are 2 % solutions, others are 5 % and others yet are much stronger, 10 %. Of course Lugol's is even stronger and can be used as well. 10 to 20 drops of a 5 % solution to a 3 gallon bucket is what is usually recommended but it is best to check with someone in the know.
Note that overdosing on iodine can be a reason for bleaching (personal comm. Bruce Carlson) and only increases the problem. Dose the water correctly.
The best is to start with 10 drops of a 10 percent solution and repeat the bath a few times over a period of several hours. This will usually take care of the problem.