Here's how I do my eggs:
Assemble your tools. I use tea-light candles, and the kistka/stylus tools for melting my wax. I prefer the tinted beeswax (that square thingy in the corner), because it is easier to see your wax lines on the egg. Cover your work surface with paper towels, plastic or newspapers. Have a bowl of water ready in case you set something on fire. (It happens!) I blow out my egg shells, and then seal the ends with wax or masking tape.
Lightly draw your design on the egg with pencil. If you make a mistake, DON'T ERASE. It changes the surface of the egg, and the way the egg takes the dye.
Scoop some beeswax up in the cup of your stylus, and hold the stylus next to the flame. When the wax is molten, draw on the egg with the stylus. I try to remember to lay off the coffee before doing this.
Drawing with the wax. THE DREADED BLOB! I find it helps to off-load your stylus after you've loaded it with new wax. I tend to get a blob when there's fresh wax in the cup. You really can't scrape your blob off, so just be philosophical about it. Nobody's perfect, right?
Hold your egg in paper towels. I find that my fingers get a bit waxy, and this wax residue can get on the surface of the egg, and keep the dye from sticking.
The egg has been dunked in the first color -- orange. This first application of wax will keep dye off the surface of the egg, and thus retains the original color of the eggshell. In this case, I'm working with a brown egg. Dry your eggs with paper towels after dyeing. The wax won't stick to a wet eggshell.
More wax has been applied, and the egg has been dunked in red. The brown egg color and the orange have been covered with wax. The next application of wax will cover -- and preserve -- the red color that is now on the surface of the egg.
Applying more wax.
The final color, in this case black. I label all my dye containers, because the darker colors all look the same.
This is the "magic trick" part of the process... Melting away the wax and revealing your colors. Hold your egg next to, not directly over the flame. If you've sealed the ends of your egg, unseal them. Eggs can explode from the heat and pressure of the flame, and that's heartbreaking! Wipe the melted wax off your egg with clean paper towels.
The completed egg! If you want to hang up your egg, break a toothpick in half and tie a loop of thick-ish thread (button or upholstery thread works well) around the toothpick. Gently shove the toothpick inside the egg, wiggle it around and pull the thread taut. The dyes are not light-fast, so keep your egg out of direct sunlight.