I have been using locally produced, straight-from-the-hen eggs for a while now. I am very fortunate to live near several folks who keep flocks of chickens. My primary egg source has a pretty large flock of layers this year, so I have been enthusiastically reaping the benefits.
A lot of people are trying to find and use local eggs these days, and I strongly encourage you to do so. They are usually similar in price to the "cage free" eggs you can find at you supermarket and the quality is significantly better. In my area, I pay between $2 and $3 for a dozen eggs, which is a significant value considering the "cage-free" eggs I get at the supermarket cost at least $3.99.
Poached, scrambled or omeletted, truly fresh eggs will behave better than the eggs you're used to. They sit up higher in the pan, the whites are tighter and won't spread through your poaching water. And souffles ... oh ... your souffles will rise higher and will be so much more delicious and golden.
Hardboiled eggs can be a little frustrating (albeit more delicious). HB eggs are easier to peel when they are "older": a pocket of air forms between the shell and the membrane holding the egg itself. The older the egg, the larger this pocket and the easier it can be to peel the egg. That said, a farm-fresh egg held in your fridge for a week before boiling will still be weeks fresher than what you get at the supermarket.
The major challenge that these eggs have posed for me has been in baking. When you buy eggs at the supermarket, you buy a carton of "large" or "extra large" or "jumbo". Well chickens don't lay only one size egg. So, your farm-fresh carton may contain eggs of many sizes.
These eggs are from the same carton. No problem for scrambled eggs or an omelette, but a significant issue if I want to bake a cake.
If you intend to bake with your eggs, you need one or two pieces of special equipment. Don't worry - you probably have one of these items, and really should own the other.
You need a scale. Don't own one? You should, you really should. Trust me. A relatively inexpensive one is here.
You also need a measuring cup that shows ounces and/or tablespoons. I like this one.
Most baking recipes call for eggs that are graded "large." A large egg weighs 2 ounces in the shell. So you can weigh the eggs from your carton and use the ones that weigh 2 ounces for baking. Easy, sure. But if your eggs are like mine, you seldom have enough 2-ouncers in the carton and therefore you need to measure eggs by volume.
A large egg out of the shell is about 3 tablespoons: 2 tablespoons of white and 1 of yolk. A tablespoon is 1/2 an ounce by volume, therefore 1 large egg = 3 tablespoons = 1.5 ounces. As eggs get larger, the volume of yolk and whites goes up proportionally (in general).
I will say that frequently the yolks in my fresh eggs are much larger than those in a supermarket egg. Some if you need egg whites or yolks for a recipe, make sure you what you need by volume: 1 yolk = 1 tablespoon = .5 ounce and 1 white = 2 tablespoons = 1 ounce.
So when you are ready to bake with your eggs of many sizes, take out your trusty measuring cup and crack your eggs into it.
In this instance, I needed four eggs for my recipe. (Four eggs = 4*3 tablespoons = 12 tablespoons = 6 ounces.) As you can see, three eggs fit the bill. In this case, I used the little bit of extra egg in the recipe, if you need to be super exact, just beat the eggs and pour off the extra.