Again, we are entering the realm of personal opinion, and the methods I will outline are based off of my experience and the experience of smokers across the country. Before I begin, let me give you a tip if you're new to the cigar world: don't inhale! Your mouth and nose have more than enough capillaries and receptors to get the full flavor out of the cigar. I do have many customers who inhale, but they are of a formidable coal mining, nail banging breed and are insane. Even if you are a chain smoker, inhaling your first cigar will have you calling up Ralph on the big white telephone quicker than you can say "Belicoso."
Almost every time I give a cigar to a friend who is a cigar novice, they start puffing away like God gave last call. This is, in my opinion, the worst way to smoke a cigar. As I mention in the cigar lighting section, smoking a cigar hard and fast will cause too much heat in the cigar and will bring more tar and nasty stuff out of the tobacco leaf, leaving you with a bitter, acrid taste. I feel that a cigar should be smoked just hard enough to keep it lit. This will make the cigar burn coolly and evenly and give you the best flavor. If you are a pipe smoker as well, you know that when you smoke your pipe too quickly, the tar and moisture of the pipe tobacco comes up into the mouthpiece and leaves you with a shot of bitter, salty liquid that is not very pleasant.
My favorite technique is to take a long, easy draw off of the cigar to fill my mouth with smoke. I keep it in there for a moment to introduce the smoke to my palate, but the mouth isn't the only body part that should benefit from the smoke. If you are blowing the smoke out really hard after taking your draw, the smoke won't have an opportunity to reach your nose and you're missing out on the full experience. What I like to do is let the smoke naturally escape out of my mouth and drift up into my nostrils. I don't suck in the smoke with my nose, just let it drift into my nasal cavity. It's a real pleasure to get all of your senses in on the party.
Also for those of us who need a bit more punch, many people will take the smoke in their mouth and blow it out of their nose through the back of the palate, instead of having the smoke come in the nostrils. This gives you a much fuller bodied flavor and gets more of the capillaries and scent receptors in on the game. How you smoke a cigar (or don't, many people also opt to chew on their smokes without lighting them) is up to you, but if you follow these tips, your introduction into cigardom will be a much smoother process, and a more enjoyable one.