With imagination, scissors and tape... and of course everything else you need to dye eggs, you can personalize and stylize your eggs.
A predetermined in progress egg dying session
Scotch tape (frog tape works better)
Marker (fine point) if you need to draw your design
Step 1: Plan Your Design
There is not much to be said past the point of the pictures and intuition, but I will mention a few things.
Your design is limited to your ability and your supplies. Some designs are simple and straight forward, others are more complicated and require some thinking. The Autodesk logo was a multi step dye and I had to think about which sequence I needed to remove tape in order to get the right colors at the end.
In addition to considering colors you have to be able to create and cut the designs out of tape while working with the topography of the egg. The smaller the design, the easier to fit on the egg, but the more difficult to create. I did several design using scotch tape and it worked pretty good, but If you can get frog tape that is used in painting, you will likely get better results.
One thing I wish I had was one of those hole punches that create shapes like bears or stars or ducks. That would have made excellent cutouts.
Step 2: Dye, Then Remove Tape
This step is as easy as it sounds. Just dye in what ever order and colors you planned and then remove tape and dye as necessary.