If your wood is already wet or green covering it with a tarp is usually pointless and will just encourage mold. It’s best to let it dry first in the open air or under a roof type of structure. Covering your wood with metal roofing is a great alternative to tarps or plastic sheets.
http://firewoodresource.com/faq/how-to-store-and-season-firewood/
Knowing how to season firewood and knowing how to store firewood to keep it dry will make your wood will help provide better quality dry wood and can save you money. Dry firewood burns cleaner with less smoke and creosote and produces more heat from less wood.
http://firewoodresource.com/faq/how-to-store-and-season-firewood/
Seasoned Firewood. If firewood is seasoned, dry and ready to burn, then it should have a tarp over the top of the stack to protect it from the elements. However, do not cover the sides of the stack with a tarp, or the wood may rot. Even after the wood is dry, the stack needs good air circulation to keep moisture out. Although it seems counter-intuitive, wood will stay drier with just the top covered than it would if the stack were covered all the way to the ground.
http://www.ehow.com/info_8761193_firewood-cover-vs-not-covered.html
Sheds. A shed or lean-to is one of the best types of firewood cover. Even freshly cut wood can be stored under a lean-to or in a shed, allowing excellent circulation and preventing mold or rotting wood. Storing wood in an enclosed garage is less ideal, since the drying wood can create a musty smell in an enclosed building.
http://www.ehow.com/info_8761193_firewood-cover-vs-not-covered.html
Only cover the top of the pile so any moisture that does get in can escape out the sides. If you get wood that is wet or green, it is best to choose a sunny location to help dry it. And if you can put it in a place where it will also be exposed to more wind, that is all the better. It is common for people to want to cover wood that is stored outside when they get it.
http://firewoodresource.com/firewood-storage/how-to-store-firewood-outdoors/
One of the most common mistakes people make is to pile their firewood directly on the ground and cover the whole pile with a tarp or plastic sheeting all the way to the ground. Covering the whole pile all the way to the ground just seals moisture inside and encourages mold and decay.
http://firewoodresource.com/faq/how-to-store-and-season-firewood/
But dry wood should be covered before any stretch of wet weather if it is close to time to burn it. Covering firewood with a tarp is probably the most common way to cover it. This can work fine, but it is best to leave the sides of the pile uncovered for air flow.
http://firewoodresource.com/firewood-storage/how-to-store-firewood-outdoors/
Stacked wood takes up less space, looks nicer and can be easier to cover. Keeping the wood off the ground is important, especially away from soil contact. Wood will absorb moisture from the ground and dirt will stick to the wood and make a mess. It can also cause the wood to decay.
http://firewoodresource.com/firewood-storage/how-to-store-firewood-outdoors/
But the advantage is, wood can dry faster when it is outdoors from exposure to sun and wind. Methods of storing firewood can be different, depending on whether the wood is already dry or not, and what the weather will be like that time of year.
http://firewoodresource.com/firewood-storage/how-to-store-firewood-outdoors/
If you store your firewood in a shed it is best to let it season outside in the sun before putting it in the shed. When stacking firewood safety should be a priority. Make sure your stacks are stable so they will not tip over. Stacking firewood more than 4 feet high is asking for trouble.
http://firewoodresource.com/faq/how-to-store-and-season-firewood/
what is best method to cover firewood
A shed or lean-to is the best method to cover firewood.   The best method to cover firewood is through a shed or lean-to.