I found this blog post that has several options to build. The most important thing if the storage is near you home is to build something that keeps the wood off the ground, than will discourage termites. Also, if it rains a lot where you live you'll want to make sure you have some sort of cover on the top at least. https://morningchores.com/firewood-shed-plans/
Kind of depends on where you live and what you have to work with.
In the pacific northwest we get a lot of rain so a dirt base isn't the best idea. We poured a concrete pad, used 4x4's that were first painted to protect them from the elements and metal sheets for the roof.
Take probably sounds like we went a little overboard just for wood storage but that came in very handy. The cement pad allows us to not have to wad thru mud in the winter. The roof is good to allow the wood to dry or cure without getting soaked and it keeps us dry when dragging wood in in the winter.
We kept is open on all sides. That allows for easy access to clean and stack firewood as well as hauling it in. Being open allows us to spray for bugs also. As well as good ventilation and air flow.
Anyway the wood shed did just fine in a freak snow storm we had many months ago. It was built so well the several feet on snow that piled up didn't cause any problems. Which brings me to the subject of the roof again. We went a very steep pitch and are glad we did. Just keep in mind the direction and how hard the wind blows in your area. Being open on all the sides the wind blows thru the structure and not against it.
I you want you can make holes in the cement pad when you pour it. These can hold removable metal stakes. These are great for using when you are stacking wood. It just give a little more stable support.
Another option (much cheaper) is to use a firewood rack and cover it with a tarp.
We did the major build and ended up putting room for a chicken coop and workshop underneath. If you are going to build make it bigger then what you think you will need because you will fill it up fast. Problem with just throwing a tarp over wood is the the wind will not be your friend. I have chased down many loose tarps and if you tie them down VERY well it is a hassle to untie and retie every time you need a piece of wood. And we use wood a lot in the winter. We don't have a furnace and wood is our only source of heat. Believe me if you live where is rains that bottom row of wood is going to be water logged and if placed directly on the ground it will get muddy too (even with some type of cover).
What works for one person (where they live) might not work for the next. You figure out what you want out of this and make this the most convenient for you. We needed a big covered area and incorporated the wood storage into that structure. I have never regretted over building but have regretted many many times not building big enough. But do what is right for you and what you have to work with.
Not a shed but I just built a firewood holder out of 2 cinder blocks and four 2"x4"x4' pieces of treated wood. Inexpensive, easy, quick. I cover mine with a tarp.
It looks much nicer with stacked logs than with the random sticks that I have in there.