Mound up the dirt on one side of the path so it slopes down 1/4 inch per foot to the opposite side, rendering it slightly slanted. This will allow for water to runoff the path. You can also crown the path by making the middle 1/2 inch higher than the sides, causing water to run off the sides.
Walk the path once a month and remove any obstacles that have fallen onto it. Remove rocks or branches that could cause tripping. Rake up fallen leaves.
Fill in low spots with gravel. Tamp the gravel down with a shovel and cover it with soil. Low spots are especially common after rain and snow storms.
Prune any trees with branches that overhang the trail. Maintain an 8 to 10 foot overhead clearance, removing any branches that hang lower. Do your pruning at the time of year best suited to the tree species. Always prune back to a branch collar.
Take your pruned branches off the trail and leave them on the ground to decompose. You can also chip them with a chipper or shredder and use them for mulch.
Pull up weeds growing in the path as they occur. You can alternatively spray the path with a pre-emergent herbicide in the spring, which will kill weed seeds before they germinate.