Be patient, and keep at it until there's a glowing ring all the way around the cigar's tip. Once the cigar is lit, gently blow on the embers to create a smooth, completely rounded ash. Then, raise the unlit end of the cigar to your mouth and take the first puff. Many aficionados blow the first puff out through the cigar in order to avoid unsavory flavors such as sulfur from matches or gasses from lighters. No one, of course, should ever apply more than one outward puff.
Some purists think that it's shameful to ever have to relight a cigar.
Realistically, even the best cigars will go out on those occasions when the conversation becomes so absorbing that you forget to take a puff for a couple of minutes. It's no worse to have to relight a cigar than it is to have to fish a bit of cork out of a fine glass of wine. It will generally take you less time to relight an already-warm cigar than it does to light one for the first time. Do not, however, intentionally let your cigar die out and then relight it the next day. This will lead to stale, harsh flavors that will ruin your fine memories of the first few puffs.