This will run you 20-30 dollars. Buy these supplies from an actual Tobacconist, like a cigar shop. Some gas stations or grocery stores sell pipes and pipe tobacco, but they're low quality and not worth smoking. An experienced Tobacconist will be able to guide you towards a proper tobacco. Just tell him that you're new and he'll get you something easy to smoke. Expect to pay around 10 dollars for 2oz.
For the pipe itself, get a Missouri Meerschaum brand corncob pipe. That is the only brand worth considering at this stage. They are cheap and smoke very well. Bent stems (the part that you put in your mouth) are typically more comfortable, but some prefer the aesthetic of straight stems. Pick one that you like the look of. Expect to spend 7-12 dollars. After you buy it, take the stem out and pull out the filter, which is a long roll of paper. We don't need it.
While you're at the Tobacconist, pick up pipe cleaners and a tamper tool. Pipe cleaners, as the name implies, clean your pipe after you're done smoking. It's good habit to use one every time. A tamper is optional, and you can get away with just using a regular nail (or your finger), but theyre convenient and fairly cheap.
Put the tobacco in your pipe and smoke the damn thing. That's only half a joke. I find a lot of people spend too much time worrying about proper technique and trying to nail a specific style for how to pack the perfect bowl. Don't worry about trying to copy a specific method. Here's what to do:
That's it. Pack it looser than you think you need to. The ideal is to compress it just enough that it takes most of the springiness out of each chunk of tobacco. Fill it up until the compressed tobacco is just beneath the rim of the bowl. The tobacco will expand when you light it, so you want to give it a little room to expand. Take a test draw here, without lighting it. If you feel any resistance compared to when it was empty, dump it out and try again. You will have an easier time with tobacco that's too loose compared to tobacco that's too tight.
Now we need to light it. Grab your lighter. A soft flame lighter is like a typical zippo or bic lighter, where the flame is like a match. Do not use a lighter like a cigar lighter or a torch, you'll scorch the tobacco. Put the pipe in your mouth and inhale while very lightly touching the flame to the tobacco (note: inhale into your mouth, NOT YOUR LUNGS). The tobacco will expand, probably coming up and over the rim of the bowl. Tamp the tobacco down with the tamper (the part of the tool that looks like a nailhead) and then do the same lighting process again. Let the weight of the tamper do the work, don't apply pressure. The flame should circle around the top of the tobacco evenly, and when you're done the top layer of tobacco should be blackened and embered. Always err on the side of 'too little flame', and go slow with it. Scorched tobacco tastes terrible. That's it as far as lighting goes.
Smoke it slowly. You aren't going for big cigar-like puffs here, don't be motivated by a big cloud of smoke. The analogy is to sip it like wine instead of chugging it. If you're smoking it too fast, you'll have two signs to slow down. One, it'll start tasting really sour. Two, the bowl will heat up beyond what it should. You should be able to press the bowl against your cheek and hold it there. As I said earlier, do not inhale into your lungs. We're looking for taste here, not a nicotine buzz (although you might get one).
The pipe will probably go out at some point. No big deal. The ash on top is very light, and you can either tamp it down or dump it. You should probably tamp it first, because sometimes unsmoked tobacco will dump out along with the ash. Tamp it down until you feel even a little resistance, then just light it again in the same way. If you dump it, invert the pipe and gently knock it against something. I've found that holding the pipe in one hand and smacking the hand that holds it is a decent method, and you can do that to avoid any pipe damage. Unsmoked tobacco will, for the most part, stick to itself and defy gravity.
When you get about 80% of the way through the bowl, dump it. There will be a little left in the bowl that you can smoke. When you start reaching about 95% of the way through, a fresh corncob pipe will start tasting very different, almost corn-like. You'll notice it right away. Take a few more puffs so that the bottom of the bowl can char, and then dump it. You've successfully smoked a bowl.
Immediately after you're finished, take your pipe tool shank (the long skinny part) and gently pull the remaining bits out. You want it to be clean of major debris. Don't scrape anything, you're just pulling the loose bits out. Then you can run a pipe cleaner through the stem. Take a paper towel and swab the bowl to get anything else. Do not pull the pipe apart while it's hot. It will warp where the stem fits into the shank (the wood part), and it won't fit together properly. Let it cool down completely before you take it apart. That's it.
It's a good idea to drink something while smoking. Tea or coffee or water are all good choices, but not alcohol. Alcohol damages your mouth a little bit, and smoking damages your mouth a little bit. Normally that isn't a big deal and you'll heal just fine, but the damage from both is multiplicative, not additive. If you want to have a dram of scotch or a beer with it occasionally, that's fine, but I don't recommend making a habit out of it.
Eventually you may want to branch into non corncob pipes. The Pipedia is a great resource for materials and styles. Corncobs can generally be smoked a bunch, but other materials will want a day or two to rest before you smoke them again.