Dig with holes that are 12 inches wide and go as deep as the frost line of your area. The frost line would depend on your location, so you have to check a frost line map. Frost line maps are available online and can be downloaded. The hole will be your starter hole for the support posts of your picket fence. This will be your starter hole for housing the support posts. Each post will be inserted into a hole.
Place the first 4x4 post onto the hole that you dug in Step 1. Pack the hole tightly with gravel and dirt. Dig another hole with the same dimensions four feet away. Place the second post in the second hole and secure it in the same way as the first post.
Attach a horizontal post to the two vertical posts that are planted in the holes. Join the horizontal post to the vertical posts using 2 ½-inch galvanized screws and a drill. Ask a friend to hold the horizontal post as you drill it into the vertical post. How high the horizontal post should be located will depend on how tall your vertical posts are. For a three-foot fence, two horizontal support posts are enough to support the picket fence. Each horizontal post should be attached six inches from the top edge of the vertical post.
Attach the first picket to the fence posts. Place the first picket three to five inches from the first vertical post. Nail it into the horizontal posts using a pneumatic nail gun.
Position another picket beside the first picket that you installed. Make sure that there is a three- to five-inch space between the pickets. Nail the second picket onto the horizontal posts. Continue nailing the pickets along the horizontal posts until you reach the second vertical post.
Dig another hole four feet from the second vertical support and place another vertical post in it. Then attach the horizontal posts between the second and third vertical posts. After attaching the horizontal posts, nail in the pickets in the same manner that you attached them in Step 5. Continue this process until you reach the desired length for your picket fence.
Paint the fence any color or stain you desire.