Smoking cigars, although frowned upon in many areas, can be great because it gives you something to do with your hands and helps you to look refined. Also, it's rather annoying to some people whom it might prove fun to annoy. Here's the lowdown:
Step one: You have got to buy cigars. Stealing isn't very nice, and growing/rolling your own is insane. So buy them. Don't buy cigars from the corner store - they usually have a very limited range of cheaper cigars. You will probably need to go to a tobacconist or specialist cigar store. Try to find one nearby, where the staff are kind, not snooty (unless snooty is your thing). They will have a humidor which is a device for storing cigars at the correct temperature and humidity. A humidor can be small enough to hold just a few cigars, or large enough to hold thousands. The store may even have a walk-in one. The first time you walk into a humidor is great, because it's like stepping off a plane in Cuba. The air in a humidor is normally around 73% humidity, and it's quite warm. Okay, pick out your cigar. There should be a cigar in there for almost any price range. If you want you could spend a week's wages on a vintage Cohiba, but you really don't need to. You can have a really great smoke for less than the price of a meal. Buy it, thank the people, and go.
Step two: Find some place to smoke the cigar. A lot of places will not let you smoke them. Some countries may disapprove of smoking in public places; others, such as Canada, may have 'cigar-friendly' establishments. Plus, there's always home. Go wherever you're going. Have a drink. Single malt whisky goes well with a cigar, as does brandy, but beer would be fine too.
Step three: Cut it. Yeah, you'll need to cut the cigar, unless you were smart enough to get them to cut it at the store, but you may develop a style that you like, so then you'll have to do it. There are lots of ways depending on your preference, but the most basic would have to be the guillotine type cutter which has one or two blades to chop the end off. It's pretty easy, and you can buy one very cheaply. Take it and cut off the end (the rounded end, normally closest to the band). How much you cut off depends on you. For an easy draw (ie you do not have to suck much), cut a hole nearly as big as the body of the cigar, the smaller the hole, the harder the draw. Cool? OK.
Step four: Light it. This is where the 'smoke' bit comes in. You can use whatever you want, but most serious cigar smokers use a butane lighter or cedar matches. Avoid petrol lighters as these may impart an unpleasant flavour to the cigar. Butane lighters burn a very pure flame, and will not leave any residue on the cigar which can change the flavour. Cedar is what the cigar is stored in, so a burning cedar match imparts a flavour that you are going to get anyway. Whatever you use, try not to stick the end of the cigar actually in the flame. Instead, hold it a centimetre or so over the flame, rotating the cigar. People may laugh, but you will be the one laughing when your cigar burns evenly, and theirs burns on a forty 45° angle. Rotating evenly heats the end. Reflect on this as you do it. Without ever touching the flame, the cigar will start to smoke; keep rotating, until it starts to glow, then (and only then) should you put it in your mouth, and take a draw (actually a few short draws). Now it will be burning, and you can lose the lighter or match, and just focus on the cigar.
Step five: Smoke it. Some key ideas here: do not hold it in your mouth. The end will become covered in spit, which will seriously affect the draw, and will also cause a lot of tar and nicotine to collect there, and be deposited on your lip. Only take a draw every 30 seconds to a minute. You shouldn't be in a hurry, drawing too often will heat it up so much that it will get a weird minty tar taste that will make your tongue feel funny. Do not inhale! Cigars have way more tar than cigarettes. This means, as any frequent pot smoker knows, that you will start coughing up brown/black gunge after a year or so. Don't constantly flick the cigar to drop the ashes, only when the ash is approaching an inch should you be concerned about it.
Step six: Putting it out. It is completely safe to let a cigar burn itself out. It only takes a few minutes, is much cleaner than stubbing it out, and leaves less of the 'after cigar' smell in the air. Just set it in the ash tray and chat with your friends, or settle your bill. Whatever...