Welcome to the pipe and all those flavours and aromas...
There is a very good article on the Pipes Digest web site on how to pack and light a pipe, but I'll add my own comments too since we all do it slightly differently and sometimes different descriptions will just click for different people. It took me about six months to get really good at packing my pipe—partly because several of my first pipes have fairly deep, narrow bowls, and these can be a little trickier. Many folks get the hang of it after just a few times, and sometimes even the first time!
The pipe. Understandably, you may not want to invest a lot in something you're not sure you're going to like or continue. However, if you can start off with a not-so-cheap pipe, so much the better. Some cheaper pipes do turn out to smoke quite well, but not all. Here, I'm speaking mainly of briar (wood) pipes, and am leaving meerschaum and clay pipes out of the discussion for now. Corncob pipes are also a good option if you just want to try pipe smoking—they are very inexpensive and require no breaking-in. They do lend a different taste to the smoke, a taste which I generally find more compatible with natural or the so-called English blends, than with the flavoured and sweetened blends.
Cheap pipes sometimes lead to bitter tastes and wet or hot smokes, but sometimes these effects are merely a result of a new briar not being broken-in. Before you blame your pipe, consider that the problem may be caused by your smoking technique or by overly moist or dry tobacco. With a bit of perseverance, you do get better at figuring out what is wrong if you have a smoke that isn't as enjoyable as it should be. If you're not sure, always smoke as slowly as possible, and that cures many pipe problems.
The tobacco. Tobacco choice is important. In my case, at first I wasn't trying the kinds of tobaccos that I would be likely to enjoy, but I had no way of really knowing that. I had always liked the aroma of the sweet-smelling tobaccos but I found they lacked something when I tried smoking them. I finally tried a couple of natural, English-style blends, despite warnings that these were for more serious, seasoned pipe smokers only. Surprisingly, these tobaccos provided the kind of taste experience I was somehow hoping for. Be forewarned though that natural or English-style blends don't usually have exactly the same degree of sweetness in their aroma, and that they're not for everyone. Only experimentation will help you figure out what you like and don't like. Trying new blends can be a lot of fun, but no matter what, always keep some of your favourite blend on hand in case your sampling doesn't go well!
There is a myriad of different pipe tobaccos available with different flavours and smoking qualities. However, you are not totally hopeless as to where to start—just take the plunge and enjoy. If you have a taste for sweets, why not start off with something commercial and easily available like Sail, Captain Black or Amphora, or ask your tobacconist for their recommendation. Some folks stick with these blends forever, but others find much pleasure in the elusive search that perfect tobacco.
If you have a taste for stronger or more bitter flavours in coffee, chocolate, tea or beer, you should try a light English blend as your first tobacco instead of a sweeter one. Better still, start with a pouch of each of the two types. Just don't smoke them in the same pipe if you can avoid it ... Smoking an English blend in a pipe used for aromatics often tastes rather weird, and vice-versa. Let your pipe take on the flavour of your tobacco for a while and then judge the tobacco. Of course, that doesn't mean that first impressions aren't lasting.... If you're smoking a fairly moist blend (like most flavoured tobaccos), be sure to pack your pipe looser than you would a drier, natural English blend.
Packing the tobacco in your pipe. If you've already smoked your pipe, cover up the bowl of the pipe and blow through the stem in case there are small bits of tobacco that are blocking the passage and which could clog your smoke.
I find that there are two key aspects to packing a pipe correctly. First, the tobacco should be only "somewhat" tight in the pipe—it should still be springy to the touch on the surface. Second, the pipe should be loosely in the bottom half of the pipe than at the top, so that it doesn't get too tight down there when you tamp it while smoking.
Start by taking a wad of tobacco that looks like it might be a bit more than enough to fill your pipe. If the tobacco seems really stuck together, fluff it up a bit before you do this. Hold your pipe over the pouch (or tin) so that the pouch catches the tobacco that falls while you're filling it. Push the tobacco in until the pipe is full and a bit of the tobacco is overflowing over the top of the pipe a bit. Don't cram it in tightly; just make sure the pipe is well-filled. Slowly and carefully fill the pipe as if you were trying to measure how much tobacco the pipe would hold under "average" circumstances, not how much you can cram in.
Your pipe should now have some (or a bunch of) tobacco sticking out of the top and may look like it needs a haircut. Pull most of this off, then take your pipe tool (a "tamper" available at your pipe shop) and *gently* push any loose ends down into the pipe. This way, your tobacco ends up a bit more tightly packed on the top than underneath, which is what you want. Touch the tobacco on top lightly with your thumb. It should feel somewhat springy.
Lighting your pipe. Put the pipe in your mouth and take a few puffs of the unlit tobacco. Not only should it taste good, but you shouldn't have to apply much suction to get air to pass through it. It should only give a little resistance, like drinking liquid through a straw. If you find that you have to draw hard on it, empty it out and start over— you have packed it a bit too tightly and it will not smoke well. Just pry it out slowly with your pipe tool.
Now, the fun part— lighting up! Big wooden kitchen matches work well, as does a lighter. If you try to use small paper matches, you may end up frustrated and with burnt fingers... As soon as the sulfur burns off, pass the lit match across the surface slowly and puff slowly but firmly, just enough to draw the flame down into the tobacco. Try not to burn the rim of the pipe. You can puff deeply, but not too hard. Hold the smoke in your mouth, but try not to inhale it. Let the smoke puff out of your mouth as you take the next puff. It can take a good 10-20 seconds to get your pipe lit. The tobacco should fluff up a little, perhaps a lot. Now take your pipe tool and flatten out the surface of the scorched and fluffed-up tobacco so that you have a flat surface on the top of your tobacco again (don't apply much pressure).
You have just completed what is sometimes called the "false light." It is called "false" because it is now time to light your pipe again. Pass the flame around the top of the tobacco, swirling it slowly to get all of the tobacco on top lit (which you just flattened). As usual, puff slowly, just enough to bring the flame down into the tobacco. This may take another 10-20 seconds or so and generate a lot of ambient smoke, which you will probably enjoy. Now you're on your way... your pipe is lit. Take a slow deep puff every 5-15 seconds or so—more often if the pipe seems to be going out, less often if the pipe seems to be heating up a lot.. You can either hold the smoke in your mouth for a few seconds and just let it drift out and stop there, or you can take a puff, keep the smoke and the pipe stem in your mouth, then a few seconds later, take another puff, letting the previous puff escape into the air. Some smokers will swallow a small quantity of the smoke, which causes it to escape through the nose and look like you had inhaled it. But you didn't. Some pipe smokers actually inhale the smoke like cigarette smokers, but the smoke is very strong and this is not recommended.
If your pipe goes out while smoking, no big deal, just re-light—this is pretty normal. Especially at first, you may need to re-light frequently. It's always better for your piep to go out from time to time than to prevent it from going out by smoking it hot. Furthermore, there's no need to panic and re-light your pipe the second it goes out if you don't feel like it or if you're busy doing something. You can come back to a partially smoked pipe a few minutes later if that's more convenient. And if you're smoking a bent pipe, you can carefully put your lit pipe in your pocket when you enter a non-smoking establishment and it will self-extinguish rather quickly. Every 5 minutes or so, or more or less, tamp down the tobacco a little, just enough to crush the ashes on the surface and to make sure that the tobacco that is lit is touching itself and continues burning. You don't want to apply so much pressure that the tobacco underneath gets further packed.
As the tobacco burns further down, the pipe will heat up. It should get warm, but if the pipe starts to get hot to the touch, let it go out for a few minutes to cool down; you might be smoking it a bit too fast. Hot smoking can cause the tobacco to become bitter, in addition to being uncomfortable on the tongue. As well, it may create moisture build-up that is very unpleasant if drawn into the mouth (which is particularly easy to do if you are smoking a straight pipe).
If you are smoking a brand-new pipe, it will need to be broken in. Smoke only half bowls for a while (at least 10 times or so) until you start getting some carbon buildup on the lower sides of the pipe's bowl. Try to smoke to the bottom as much as possible to get this carbon cake built up and your pipe will smoke much better later. On the other hand, if at any time your pipe starts to taste nasty, stop. Pipe smoking is always supposed to be pleasant and there's no reason why it shouldn't always be so.
Practice makes perfect (or almost). Enjoy!