Pecan trees are native to the southern central part of the United States. Left to their own devices, they grow in rich soil along rivers and creek bottoms. Pecan trees flower in the spring, roughly 7 months before the resulting nuts are ready for harvesting.
Look at the husks that hold the nuts. If the husks have split open and you can see the nuts inside, they're ready to harvest.
Pick up any nuts that are already lying on the ground under the tree and put them in the bucket.
Spread a clean bedsheet on the ground around the trunk of the tree. Cover at least a foot of the ground beyond the outermost branches of the tree with the sheet. If necessary, use more than one sheet.
With the wooden stick, tap the branches of the tree to encourage the nuts to fall off the tree.
When you've gotten all (or at least most) of the nuts off, carefully pick the sheet up off the ground by its corners, letting the nuts collect in the center.
Carefully pour the nuts out of the sheet and into the bucket.
Take the bucket to the table, dump the nuts out on it and remove any husks that are still encasing the nuts.
Find a place indoors to store your nuts where it's dry and where pests like mice can't get to them. An airy garage or garden shed would work well.
Pick a spot in your chosen place that's not in direct sunlight. Set the screens up there by putting small pieces of square or oblong wood beneath the corners of each one, so air can circulate around and through the screens.
Spread the nuts out in a single layer on the screens and leave them to dry for 2 weeks.
Test one nut to see if it's dry by trying to bend it. If it cracks open with a snap, it's dry enough. If not, leave the nuts on the screens for another week and then test again.