Freshly cut wood is referred to as green, and is very wet, containing up to 80% moisture by weight. To dry out the wood to 20-25% moisture content so it can be used as fuel, you season it by cutting it up into short lengths and stacking it out of the rain in such a way that air can circulate freely to carry away the water as it evaporates out both ends of each piece.
Remember Granddad's wood shed? The open slat walls allowed air to circulate, and the overhanging roof kept the rain off the wood. The seasoning process generally takes around 12 months, depending upon the species of wood and the airflow, humidity and temperature of the woodshed. Once the wood has evaporated down to 20-25% moisture content level, it is seasoned, and ready to burn.
Seasoned wood doesn't always stay that way: wood is cellular, and will reabsorb water like a sponge. If you get dry, seasoned fuel wood and stack it out in the rain, it can soak up enough water to revert to its original water content in just a matter of hours. When this happens, your seasoned wood needs to be re-seasoned until it is once again dry enough to use for fuel, which can take several weeks.
You can read about the importance of avoiding burning green or wet firewood in an airtight woodstove I a previous post.
Store the Firewood Correctly!
Just throwing a tarp over the wood just isn't going to make dry wood for you. Make a bologna sandwich on some nice fresh bread. Cut it in half, wrap one half tightly in plastic wrap, and put both halves in your refrigerator for a few weeks. Compare the dry, crusty half with the bag of soggy goo, and you will be looking at a good demonstration of why your woodpile won't season properly if you cover it with plastic tarps.
This is also the reason woodsheds traditionally have open slat sidewalls: as moisture evaporates from the wood, air circulation is necessary to carry it away. Your tarps create a mini-ecosystem where the evaporated moisture condenses on the underside and rains back down on the woodpile, where it is reabsorbed.
If a tarp is your only option to keep rain off your firewood, drive tall stakes a foot or two from the four corners of your woodpile and drape the tarp over the stakes so air can flow through the woodpile beneath it. Take a few pieces of wood and stack them on top of the pile at the center under the tarp so rainwater won't puddle, and fasten the tarp to the stakes so the wind won't blow it off.