Choose a nice coloured brown egg (my chickens eggs come in many shades, a pack of free range eggs from a farmers market may yield interesting colours or shades). If desired, colour the egg with an even darker shade of brown to make it richer in tone. I used a shade of Ukrainian egg dye called "Nutmeg Brown". Nothing dyes an egg like Ukrainian egg dye, I source mine at the nearest Ukrainian store (Koota Ooma). When you buy the dye it comes as a powder and you mix it with distilled water and vinegar (for a mordant), then place it in clean canning jars and label, it will last you years if you keep it nice and clean. My favourite egg dippers are those copper hoops that come in children's egg decorating kits at Easter, you can get them for very cheap after the holiday!
Step 1: Writing the Pysanky
Dry the egg and begin "writing" on the egg with a kistka (also available at Ukrainian stores) and beeswax. Hold your kistka close to the side of a candle flame to heat it, then if you set the wax against the top in melts in. If you are unable to find a kistka, you could use other techniques such as dip and dragging wax in petal like formations, another Ukrainian/Polish egg decorating technique (this involves a ball tipped tool).
When completed with your design, place the egg in vinegar for a few moments. The vinegar will react with the calcium carbonate in the egg shell and begin dissolving it. Take the egg out every 30 seconds and rub it with your finger to see the level of etching, remove and watch the egg under running water when you like the colour, using your finger to gently rub over the dissolved shell.
Blow the egg out ( I use a egg blowing device also available at a Ukrainian store) I recommend you use a small nail with a cut end (the facets in the cut point are important) and slowly twist it while applying pressure to make holes on either end. Then enlarge the hole a bit with a larger spiral 3 inch nail (again just lightly twisting). Then insert a long wire to break the yolk and use your mouth or a rubber bulb to blow the egg out. I usually blow the egg out first (prior to decorating) in case it is a structurally unsound egg so I don't ruin my work, however, with vinegar etching sometimes I don't as it easier to keep the egg submersed and vinegar does not get inside that way. I also use a syringe to add water, shake it around and blow out again to clean the egg thoroughly.
Heat the blown egg in a microwave for 10 seconds at a time on a paper towel, until you see the wax get shiny, then take it out and wipe the wax off. The wax gives the egg a nice polish!!