Need to get it at least 12" off the ground to keep it dry. If you ever look at the side of a building and see where the dirt line is then you get the idea.
I've seen people use corrugated polycarbonate sheet for a roof over their wood racks when they're in front of their house. It looks OK. The sheet I'm talking about is what you usually see on top of people's pole barns for letting light in.
So it looked like:
two 2x4x8 spaced 12" apart with four 2x4x4 vertical. Attached to the top was two more 2x4x8 spaced 12" apart. For the roof, they bent the plastic in a half moon shape and screwed it to the top 2x4x8. They had it sitting on rounds. I usually use 8x8x16 concrete blocks.
I usually use two 2x4x8' with two pieces of 2x4x24". I space the 2x4x8' at 12" on center. I then set it on three 8x8x16 concrete blocks equidistant from each other. For the ends I use 6' T-posts. I use 9x9 tarps to cover the wood, held at each corner with a bungee cord. Not very pretty but the neighbors have to look at it and not me.