Generally, it is best to send circular saw blades out to a sharpening company to have them sharpened because these companies have the equipment and ability to sharpen the blades while keeping them perfectly round. If you try to sharpen circular saw blades yourself, you could shorten some of the teeth. This would result in some taller teeth which would end up doing all the cutting work. Without special equipment, you won't have much luck sharpening carbide tipped blades. But if you want to touch up a high speed steel blade, you can do it with a good smooth file.
First, sandwich the blade with two pieces of round plywood to hold the blade tight, without any harmful pressure on the teeth. Then, find the underside of the cutting tip with the file. You will notice that every other tooth alternates its angle, so you sharpen every other tooth from one side, and then sharpen the alternating teeth by turning the rig around and doing it from the other side. Try to take the same number of strokes on each tooth to keep them the teeth even in length. Never try to sharpen the top of the tooth. You will change the diameter of the blade too much.
The second photo above shows two different carbide teeth. You can see the size of the carbide is, itself, an indication of the quality of a blade, and a direct measure of how many times you can sharpen the blade before you need to either get a new blade, or have new teeth installed. So inexpensive carbide blades are not necessarily economical.