I just noticed today patches of brown on the leaves. What does this mean, and what do I do about it?

This is much to vague to make any diagnosis. What type of plant? All the leaves? Certain portions of the plant? Spots? Entire leaves? If you can provide more information that might be able to narrow down what's going on.

I have Martha Washington Geraniums. There are brown spots on the tops of the leaves, and some are brown on the edges of the leaves. So far the flowers are ok, but I want to find out what's causing the brown spots, and how can I correct it?

The browning could be due to several things. Evidence of it along the edges may be an indication of watering issues. While most geraniums like it slightly dry, Martha Washington geraniums tend to like a little more water so the soil needs to be kept evenly moist. Martha Washington geraniums are also a bit more finicky than other types and they are difficult to keep in the home. They don't like heat and prefer cooler temperatures. The brown spots can indicate some type of foliage disease. A strong possibility is botrytis, a fungal disease that affects the leaves and the flowers. At this point in time your best approach is to remove the leaves that areaffected to prevent further infection to the others. Be sure there is good air circulation. You might want to move the plant outside to a partly-shaded location.