I enjoy a good hike during the summer.  Have you ever hiked the Appalachian Trail?  It's a pretty popular trail in the Eastern United States.
i have heard about it but do not know much about it
Let me tell you more!  The trail itself is around 2,200 miles long and spans over 14 states. 
what state does it start and what state does it end?
It starts off at Georgia and spans all the way to Maine.  It's also home to 2 million annual visits each year as they participate in the hike.
so, is it a public trail on public land or does it also go through private land?
It goes through public land and the trail itself can be hiked by anyone.  No cars though - It's such a long trail that it's been claimed to be the longest hiking only trail in the world.  
is it free to use or do they charge a fee to use
each year.
The idea of the Appalachian Trail came about in 1921. The trail itself was completed in 1937 after more than a decade of work, although improvements and changes continue. It is maintained by 31 trail clubs and multiple partnerships, and managed by the National Park Service, United States Forest Service, and the nonprofit Appalachian Trail Conservancy. Most of the trail is in forest or wild lands, although some portions traverse towns, roads and farms. It passes through 14 states: Georgia, North Carolina, Tennessee
Appalachian Trail
The Appalachian National Scenic Trail, generally known as the Appalachian Trail or simply the A.T., is a marked hiking trail in the Eastern United States extending between Springer Mountain in Georgia and Mount Katahdin in Maine. The trail is about long, though the exact length changes over time as parts are modified or rerouted. The Appalachian Trail Conservancy describes the Appalachian Trail as the longest hiking-only trail in the world. More than 2 million people are said to take a hike on part of the trail at least once