For the Monster Swap 4, I sent a woodburnt plaque to my partner:

She seemed very impressed by the technique and wanted to know how it was done, so this is for her! Now, I expect that seasoned pyrographers will probably chime in after this. I expect and welcome that, as I really am a newbie.
First, tools:


You'll need a phyrography pen, which you can buy for about $15. They generally come with a small assortment of tips; the second picture shows the tips included with my Walnut Hollow pen as well as a few others I bought.

You'll also want some scrap wood to practice on before touching the pen to the official project. DO NOT try to cut corners here. It really makes a difference to practice first. As you can see in the picture above, the tree was originally supposed to look quite a bit different, but I found on my practice wood that that technique just would not do. This also helps you get a feel for how long to hold the tip at any one point. This makes all the difference in the appearance of a project. I dragged the pen tip extremely slowly across the wood to get deep, exaggerated lines that gave a dramatic, bold feel. Using quick strokes can allow for a gentle and wispy appearance, which is good for hair/grass/etc. The lines will also be brown rather than black and will not be very recessed. Make sure to pick up the pen as little as possible, because it is tough to hide each spot where you placed the pen down. Make continuous lines wherever possible. Another reason to use a practice piece is to get a feel for how the temperature is going to affect your method. On some pens, you can vary the temperature, but you cannot on mine (and it seems that way for most cheaper ones). For these, the pen gets hot. Really, really, really, REALLY hot. I mean it! At any rate, the amount of time you have allowed the pen to heat will make a difference, so test first! If your line ends up too dark, you can try to gently scrape or sand off some of the darkness. This technique will not always work, though, so start out light and then go darker if you feel the project needs it.

One key to remember is NOT to use pressure. Allow the heat of the pen to do the work. Pressing down will not only often result in an undesirable appearance (it's hard to regulate the pressure, so your lines will be of uneven width and depth), but it can ruin the tip. You can see in the image above that I had bent the tip of my leaf point by the end of the project (new one on the left). At times, I forget not to press down! Remember that the tips are much more malleable when heated. This effect will eventually be seen in this style of tip anyway, but using light pressure will prolong the tips' lives.

Next: the carbon layer. From the natural carbon in wood, the tips will get covered in a layer of carbon very quickly (used but slightly cleaned one on the right). This reduces heat transfer and, if built up enough, can cause ugly, black blobs of goo to come out of the wood. For this reason, keep a clean pen tip! Keep fine sandpaper next to you while you work, and clean the tip on it when it starts to get dark. Use very, very fine sandpaper, and try to minimize the amount you scrape off. This will dull and reshape your tips more quickly than you think, but it is necessary. Make sure you use sandpaper with a paper backing, rather than the cheap stuff with styrofoam in the middle (you'll know what I mean if you see it). This is because the tip will melt straight through that extremely quickly. Also, prepare for the improved heat transfer after cleaning the tip. You will not need to hold the pen in one spot as long until the carbon builds up again.
Okay, the last thing is SAFETY. I know a lot of people craft with cats running around everywhere or other roaming pets. DO NOT let them anywhere near you at all when you do this. I've dropped my pen on the carpet a couple times, and it melted the carpet in that one little spot in literally less than a second. When it comes time to change pen tips, be patient! I usually wait a bit (maybe 10 minutes?) after turning the pen off and then cool it the rest of the way with a thick, folded paper towel drenched in cold water. Do not EVER try to do this with your hands until the pen is completely cool (test the handle first, as this part gets very hot, then test as you would a clothing iron). Don't even try it with gloves that are not meant for heat. I tried this once with leather work gloves and even got burnt (although not badly) through those in an instant. Basically, I can't tell you enough how hot these pens get. Now, you probably will eventually want to wear gloves while burning, because the pen does get hot. Definitely work in a well-ventilated area. If you can, have a small fan positioned such that it can blow the fumes away from you.
WOW that was way longer than I intended it to be. I hope this helps anyone who is trying to get into pyrography! I've had so much fun with this hobby. In fact, it's very therapeutic at times!
Enjoy and happy woodburning!