There are many fine cigar makers out there. The best cigars are hand-rolled. Many of the great Cuban cigar makers left Cuba when Castro took over, but a lot of Cuban seed was smuggled out at the time they left. Cigars grown from Cuban seed stock in Nicarauga, Dominican Republic, and Honduras today are very good.
Most of the flavor in a cigar is in the wrapper. Cigars with a corojo wrapper will be stronger and fuller flavored, while a Connecticut wrapper is very mild. Maduro cigars are the darker cigars, which comes from an extended aging process, and gives the cigar a distinct (and usually very pleasant) flavor.
YouTube has a number of videos with people showing the correct way to cut, light and smoke cigars. There are variations, and everyone has to experiment to find their favorite way. For instance, there are three main types of cutter, the guillotine, the v-cut, and the punch. My preference is the v-cut.
'Experts' usually advise that new smokers start with mild flavored cigars, and try fuller flavored cigars after they've smoked for a while. I tried the stronger, fuller flavored cigars early on, and found that I preferred them. All the cigar merchants offer 'samplers' which consist of 5 to 10 cigars with one or two of several different cigars at a little discount. The samplers are a good way to start and learn about several brands and blends of cigars and find the ones you like without buying an entire box. I always suggest that a new smoker try at least two of a particular cigar before deciding for sure if he likes it or not. Even the best cigar makers will have a dud once in a while, and trying two or three gives you a chance to see if you really don't like it, or if the one was just a bad example.
Cigars International - discount cigars, humidors, cigar accessories
Cigar.com - Cigars
Serious Cigars Premium Cigar Shop Cigar Store & Accessories
This link is to a good cigar forum that you can read and find loads of info:
The Cigar Lounges at Puff