Boiled eggs

Boiled:
Put your eggs in a single layer in a medium sized pan and fill with water to a few inches above the eggs.

Set the heat to high.
When it just starts to a bubble, put the lid on and turn off the heat.

Set a timer, anywhere from 5 minutes to 10 minutes, depending on how firm you want your yolks.

When the timer goes off, use a slotted spoon or spider to move your eggs into ice water. If you plan to use or eat the eggs right away, only let them cool enough to handle, then peel while still warm.

Sous vide:
Devices vary, so you may find that these cooking times are not correct for yours. You'll want to try different times until you find what works.

Set up your circulator and follow the temperature and time suggestions listed.
Once the correct temperature has been reached, lower the eggs in with a slotted spoon or spider. When they are done, remove them with the slotted spoon or spider to ice water. If you plan to use or eat the eggs right away, only let them cool enough to handle, then peel while still warm.

Poached: Poached eggs
Good on toast, hash, or with Hollandaise/Eggs Benedict.

Soft boiled: 194 for 8 minutes. If the temperature drops significantly when you put the eggs in, set your timer for 9 minutes instead of 8.
Good as Ramen/Tea Eggs (Ajitsuke Tamago), or with toast. To warm a soft boiled egg that has been refrigerated, put very hot water in a mug or bowl (at least 180 F.) and put the egg(s), still in its shell, in for 5 minutes. Peel immediately. These are very delicate to peel, so be careful.

Medium: 165 F for 1 hour.
Good for Pickled Eggs And Beets and Scotch Baked Woodcock.

Hard boiled: 167 F for 1 hour.
Good for egg, tuna, chicken, or Ham Salad or Deviled Eggs.

Coloring your eggs:

There are two methods if you are using food items.
First, you can boil the items with your eggs. This works beautifully with onion skins, but everything else is hit or miss.

The second method (which you will always use if you sous vide) is to put the items in a pot of water alone and boil them until the color is dark, about 30 minutes.
Let cool and add a couple tablespoons of vinegar and the ice. (If desired you can filter the water, but it isn't strictly necessary.)

If you are using food coloring, you can obviously just stir it and the vinegar into water and add ice.

Leave the eggs in the colored water for several minutes, hours, or put it in a jar in the refrigerator and leave it overnight. Just keep the eggs cold. Gently stir occasionally.

Move eggs to paper towel and allow to air dry. Spice colored eggs will need to dry, be rinsed, then allowed to dry again.