You can freeze dry them, freeze them, or dehydrate them.
For freezing-
Crack one egg into a muffin tin and add a tiny pinch of salt or a sprinkle of sugar. Scramble in the muffin tin. Place in the freezer for a few hours until completely solid. Pop out and toss them in a freezer safe plastic bag or an airtight container labeled salt or sugar, depending on what you use. Put back in the freezer until ready to use.-
The salt or sugar will help the yolks not to get as gummy.
For freeze drying-
Crack eggs into a bowl or blender and mix until smooth. Pour into the freeze drying trays and freeze for 2-3 hours or overnight. The next day, place in the freeze dryer and dry according to the instructions for 24+ or until they're completely dry. Run them through a food processor until you have a fine powder. Store in a jar or a Mylar bag with an oxygen absorber.-
For dehydrating-
Scramble the eggs and cook. Place in the dehydrator and cook for 10-15 hours at 145 degrees. Once dehydrated, place in a food processor or blender until you have a fine powder.
Once they're dehydrated they'll last up to a year, and to rehydrate, add a tablespoon of egg to 1-2 tablespoons of water. This way works best in baked recipes and you may have some undesirable results if you scramble them.
Hope this helps!