There are a lot of ways to mess up a cigar— improper storage, lighting it incorrectly and so on can harm or even ruin the smoking experience. If you cut it wrong, though, you may not even get a chance to smoke it at all. A badly cut cigar can burn too hot or completely fall apart!
If you have smoked cigars before and are simply looking to improve your technique, you can skip this paragraph. But for the purposes of instruction, let's say you are brand new to cigars. The end you cut is called the head. The head is the end you put in your mouth for smoking, near the label. The reason you need to cut it is that cigars are made with a closed, sealed head to help lock in as much freshness as possible as well as to keep the structure of the cigar secure. If you don't cut the head, you cannot smoke the cigar.
Look carefully at the head of your cigar. The very end is covered by a small, round piece of tobacco called a cap, which is glued on to hold the cigar wrapper together. Ideally, you want to cut the cap without cutting too much of the wrapper, which can cause the cigar to start unraveling. Your goal is to cut the head of the cigar just enough to create a good, smooth opening though which to draw the smoke into your mouth.
When it comes to actually making the cut, you have a few options. Cigar cutters are available in a variety of types, some of which work better for certain shapes of cigar. The most common are guillotine-style cutters with both single and double blades, which simply chop off the very end of the cigar. Punches and V-cutters are alternatives that work by making either a hole or a V-shaped notch in the head, respectively. No matter what kind of cutter you use, it's vital that the blade (or blades) be very sharp.
If using a guillotine-style cutter, carefully line up the cigar beforehand so as to cut off about 1/16th to 1/8th of an inch, or where the curve of the head begins to straighten, and make the cut in a swift, precise motion.
If using a punch or a V-cutter, avoid making too deep a hole as this can negatively affect the draw. Too narrow and deep a puncture will cause the cigar to burn with too much heat in the middle, and too deep a notch can expose too much surface area, which can both harm the structural integrity of the cigar and cause the draw to be too hot.
Now that you know the basics, you can cut your cigars with confidence, and eventually fearlessness and grace. Practice makes perfect and soon you will be a master.