Beginning at the town of North Conway, New Hampshire, take Route 302 norhtwest to the Crawford Depot which will be on the left side of the road and also being at the highest point that Route 302 reaches in this area. There is adequate parking here. The actual depot is a train station. Once you've parked your vehicle, cross over the railroad tracks and look for the sign marking the trailhead. Head into the forest along the well worn trail and follow the signs towards the summit. As soon as you enter into the forest, you will see a large sign at a split in the trail. This sign has a map all of the trails in the area. Bear to the right at the split in the trail and follow the Avalon Trail, making several stream crossings, and then paralleling the stream.
From the Crawford Depot head up the Avalon Trail past the Mt. Willard Trail. Past this section the Mt. Avalon climbs very for nearly the first mile. It moderates until it reaches the intersection with A-Z Trail. At that intersection make a left on the Avalon Trail. The trail soon steepens for the next quarter mile where it then moderates for another quarter mile. There will be a short side path which goes up one steep area about 0.1 more miles to open views of the Presidentials.
Winter: Trekking poles, crampons. I recommend snowshoes until the upper part of the trail. Then change to crampons when you get to the one steep pitch. (This is coming from someone who did use snowshoes)
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