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
It's free to use as it is managed mostly by National Parks and the nonprofit Appalachian Trail Conservancy.  The idea of this trail started in 1921 and was completed in 1937.  It took only 16 years to finish this long trail!
sounds like a challenge if you want to hike the whole trail.