The best way to cut a brownie depends on the type of brownie you want, as well as how much attention you want to pay to detail. If your purpose is to present the brownies in such a way that customers will buy them, cut them in a meticulous way; if all you want is a brownie hot from the oven, a cruder approach will work just fine.
Knife and Brownie Pan
The simplest way to cut a brownie is to take a knife and cut a chunk free from the pan. It wont be pretty, but if all you're looking for is a bit of brownie to eat, then there's no sense in making it any more complicated than it has to be.
A Wet Sharp Knife
One way to cut any kind of sticky baked good without getting too much mess on the knife is by using a sharp knife and wetting it before you cut. The water will keep any sticky crumbs from adhering to the knife, where they can then come off when making a second cut and mar the surface of your brownie. If presentation is important, this cutting method can be helpful. Rewet the knife every few cuts, and use a towel to clean any brownie from the knife if necessary.
Plan Before You Cut
If you're going to be selling your brownies -- at a bake sale for instance -- cut all of the brownies the same size. Use a clean measuring tape to create lines to cut along, or cut down the middle of the pan and then cut down the middle of both halves you've created, repeating this on either axis until you have the desired brownie size.
A Shaped Baking Pan
Some people consider the crispy edge of the brownie the choice cut, and there's a simple way to create more of these choice cuts while also making your cutting work easier. Shaped baking pans, which are your normal baking pans but with ridges running parallel down one length, make cutting much simpler and make every piece of brownie a delicious edge piece.