We sell quite a few eggs and my #1 bit of advice is to
check applicable local, state, and federal laws, especially if you're selling to strangers. For example, I can't re-use cartons from the grocery store unless I were to mark out every bit of writing on it, which would be pretty ugly. Also, my eggs must be marked ungraded and mixed size. We must include a packing date on the carton, as well as our farm name and address. Finally, eggs must be stored at or below 45 degrees, and I must have a commercial thermometer in my egg fridge to prove that. I must keep a record of the number of eggs I've packed. There are certain things I can and cannot say on my packaging. None of it is actually too onerous, but it does preclude my selling at farmers markets. Not sure what state you're in, but here's a look at Ohio's laws:
http://codes.ohio.gov/orc/search/shell+eggs
My #2 bit of advice is to make up some cheap business cards with a cute logo on them and start handing them out to everyone you know. People on CL sell eggs for incredibly cheap prices--there's no way anyone around me is even covering feed costs at $1.50/dozen, but I see them advertised around her for that price all the time. But people don't want to buy eggs from a random stranger, they want a relationship if they're gonna pay a premium price. We sell eggs for $3.50 no problem, and one woman buys our eggs and resells them (home delivery) for $4.50--but people want to know who they come from. Word of mouth is key. CL is free, so keep posting there, but don't expect it to yield much.
#3--make your cartons cute. Make a logo. Look professional. People will trust you more, and be more willing to buy from you than the person who's just stuck an address label on an Egglands Best carton
#4--definitely donate any eggs that are older than two weeks to the food pantry. Customers are paying a premium price to you for a premium product. Yes, eggs can last really long in storage, but that's not what your customers are paying for and you won't get repeat business. Also, your customers will like the fact that you donate excess eggs and it will help build that all-important relationship.
Good luck!