Fast, easy and simple construction of a log store
In the past, I've used lattice layed over a 2x4 frame as a floor.  This works well to get some ventilation from the bottom.  I've also used lattice on the sides as well.  Don't worry too much about keeping the logs perfectly dry.  What you want is good airflow so that any surface moisture can dry quickly.  You probably also want to think about having a few sections, so that you can add new wood to one section, and take older seasoned wood from a different section.

I've also heard about people just nailing together four pallets to make a three sided box.  If you have a tractor with pallet forks, this also makes it easy to move wood next to the house as needed.