At the very least, just bung it on the pallets with a tarp over the top, at least it will be part way to dry. We have seasoning stacks kept in a similar way, cord wood is stacked and then covered with a tarp or tin sheeting. Starts the process before spiltting into our storage sheds for finishing.
Seeing the variety of sheds on here, it will also take a long time to build whilst you consider all your design options.
Samuri - Some of our sheds are stone built, including my own at home, but the key thing is that they are sun-trap yards with ventilation (holes) in the sheds which I think is what McM's wood cave lacked. Tend to leave the door open on the shed at home to further encourage drying.