I really love dehydrating foods.  It is an easy solution for many things in your long term storage. It is also extremely easy to do.  Folks have been drying foods for centuries.  It doesn't take much equipment and the foods, when dried, can be stored easily and take very little space.   You will need some method of drying your vegetables, a knife or a vegetable slicer and some method of blanching some of your vegetables. 
You can dehydrate most vegetables.  There are of course exceptions to every rule, but generally most will do well when dried.  Don't be afraid to experiment. 
   You can dry just about anything.  Carrots, peas, sweet corn, green beans, okra, cabbage, spinach, Swiss chard etc. I also dry tomato's for use in soups and stews.  I like drying things like green peppers, hot peppers, and onions for use later in the year when these things are out of season.
I have had problems with re-hydrating green beans in the past and asked a true drying guru for some help.  She suggests blanching and then freezing the green beans before drying.  The freezing breaks down the cells so they will rehydrate better  otherwise, they will take a couple of hours to rehydrate.
The possibilities are endless.  So what are you waiting for?  

Tips for Dehydrating Vegetables
Here's a good guide for dehydrating basics.  It should help get you started!
Food - Dehydrating Food                            
Egg Articles  
Let me put a disclaimer up here. The USDA does not recommend this method. I have tried it and it works for me. That is my choice. You will have to make your own choices.
Dehydrating Egg