Most people spend between five and seven months on the Trail. Most people start in early April from Springer Mountain. The folks from the Georgia A.T. Club advise beginning no earlier than April 15 because of the potential for severe weather prior to that.
Some people choose to go from north to south instead.
People choosing this direction generally start in Maine in June. The odds are probably in your favor if you have a certain amount of experience under your belt before attempting a thru-hike. This would include books and maps, transportation to the trailhead, food, occasional lodging, occasional restaurant meals, etc. And then of course you will need to have proper equipment. Earl Schaffer hiked the whole A.T. in 1948 and subsequently wrote about the experience in his book Walking with Spring.