The answer to that will of course depend upon your location and supply and demand in your area.
On a very small scale, to just offset feed costs for a smaller flock (10 to 12 laying hens), I've sold both eating and hatching eggs.
In my area, NW Oregon, the demand is for the designer egg types...Black Copper Marans, Cream Legbar, Ameraucana, and subsequent Olive Egger mixes. Or unique pure breeds like specialty colors of Orpingtons. Silkies and Seramas also seem to sell.
For something like the Black Copper Marans (dark brown layers) and Cream Legbars (blue egg layers) generally the going rate is $3.50 to $5 an egg and beyond, depending upon your lines. I've seen a dozen at as much as $50.
I've sold olive egger mixes from general lines at $6 a dozen as I am still developing my lines (Barnevelder over Cream Legbar). I've got a Cream Legbar pair that I'm growing out for the purpose of selling Cream Legbar eggs as those are in higher demand. (I bought those hatching eggs at $3 an egg for $18 for 6 eggs...which was on the cheap side).
As to process, choose fresh eggs daily that are symmetrical in appearance, clean (no feces or mud), and have solid shells. Medium to large eggs are best. Avoid any very small or very large. Avoid any with cracks or shell flaws. Essentially, they are your best eggs.
You should mark the lay date on the unwashed eggs and store them in a cooler area (50 to 60 degrees F...sorry don't know the Celsius) but not the fridge. You should place them in an egg carton and rotate the carton so that one corner is raised differently each day. You will need to retire any egg over 7 days old. (Eggs 10 days and older can hatch, but hatchability is reduced 50% by day 14).
Generally people contact the breeder with an egg request to allow the breeder to gather and collect the appropriate number of eggs. Sometimes the breeder has the stock on hand, other times you need to collect. I personally take orders then fill, or if I have a lot on hand, let it be known I've got some hatching eggs. I do "okay" moving my hatching eggs in spring when people are thinking about new chicks or hens are usually broody. I do most of my business with those who have a broody hen and want to set eggs under them. That market is viable as it is hard to get eggs quickly for a brooding hen and her schedule....but it is also very small. Most people go locally for that as shipped eggs are expensive and often risk the hen being not broody by the time the eggs arrive.
Selling hatching eggs is more of a sideline as I found it a lot more hassle. You've got a very narrow time frame for the hatching eggs, and you must handle them differently than eating eggs. While small holders are exempt from FDA egg handling rules in America if we sell directly, most of us tend to follow them to be safe. FDA allows 30 days for facilities in America to gather and box eggs before they must be sent off to the stores. In America they require they be washed and sanitized (although Canada may be different). At the store, the eggs can remain for....if my memory serves....another 30 days?....before they must be placed on shelves for sale. The average age of an egg in American stores for eating is about 6 to 7 weeks. Eating eggs stay fresh for months in a refrigerator.
But not so with hatching eggs. You've realistically have a 7 day window of safety for that egg to be at its best viability to ensure fertility for hatching. That means you have to be willing to swap out eggs regularly. Then what do you do with the eggs that are no longer sell-able for hatching? You've not stored them in the fridge for 7 days. You've also got dates marked all over them. I end up eating those as I don't like the idea that I would be selling eating eggs that hadn't been handled according to FDA processing standards....and a bunch of marked eggs looks odd (pencil doesn't always wash off easily...marker assuredly doesn't).
I find selling eating eggs much easier and far more lucrative with a lot less potential waste. But there is a market for the designer eggs or pure breeds that are unique or difficult to find.
Good luck with your new venture should you decide to undertake it.
LofMc