I’d go for leaving the band on, simply because if you’re not practiced with cigars you may look silly trying to get it off unless it slides easily. And, one other function of the band (especially on cheaper cigars) is to help keep the wrapper on. I’ve had some amazingly expensive cigars start to unravel when I took the band off.
When you clip the end of the cigar, you want to achieve two things: First, you want to make a hole through the wrapper so you can draw smoke, and second, you want to leave part of the cap on so the wrapper doesn’t unravel. Clip as small an amount off the end as you can to achieve this. If you try to clip too fine, you’ll squish the part you’re trying to clip or the clipper will slide off. Clip too much, and you’ll pull the cap off. You should be able to tell by feel if the cutter has a good grip and is cutting through.
One of the easiest ways to get a cigar ready is to use a bullet cutter, which looks like a .45 or .38 brass shell casing (and that’s often what it is, with sharpened edges). You simply put it against the end of the cigar and turn it. It will cut a nice hole in the wrapper of the perfect size. I had one of those for a while and it beat the hell out of a regular cutter.
At a social, they may have a tray with seveal cutters on it available for use. If you see the little bullet casing, try it. It’s the easiest for a new person to use.
To light a cigar, you should first hold it out and heat the end while turning the cigar, to get the entire end smoldering. Then put the cigar in your mouth and light it again while drawing. The purpose of this two-stage process is to get an even burn so the cigar doesn’t start burning down one side more than the other while you smoke it. On a large-gauge cigar like a Hemingway or a Robusto, this is necessary. On a thin cigar it’s not, and you can light it like a cigarette.
If you are completely new to cigars, I would add a couple other pieces of advice: First, take your time smoking it, and only after a large meal. Second, don’t inhale. If you’re going to be smoking a real Cuban Cohiba, the thing will knock you on your butt if you smoke it quickly. A cigar like that can be smoked over a period of a couple of hours.
If you aren’t a regular cigar smoker, a Cohiba may not be your best choice. You might be better off getting a cigar that is less strong, like a good quality Macanudo. Cigars from the Dominican Republic are usually the mildest, with Honduran cigars being somewhat stronger and Cuban cigars being strongest of all.