Fence posts are generally solitary items. Only one is needed for a given stretch of fence, but if you have a need to connect two posts together, you want the connection to be as strong as possible. Due to the size and weight of 4-by-4 fence posts, creating a strong connection will require much more than just angled screws and wood glue. Countersunk lag screws will have the ability to keep the two wood pieces together without ruining the straight facade of the posts.
Suspend a post between two tables. Make marks on the top face where you want to install the lag screws. Three screws should be fine, although you can install four if the post is more than 6 feet tall. The screws should be spaced evenly, but keep them clear of any area where other fence hardware, like rails, will need to be installed.
Drill holes through the 4-by-4, on the marks that you made, with your 3/8-inch drill bit. Then go back and drill the same holes using your 1-inch drill bit -- but this time only 1/2-inch deep.
Place the 4-by-4 you just drilled on top of, or next to, your other post. Align them as they will be when they are installed. Place a long nail or drill bit through the small hole in the drilled post, and tap it with something hard, like a hammer. This will leave a mark telling you where to drill on the second post. Repeat for every hole on the post.
Put your 3/8-inch drill bit back on your drill and wrap a piece of tape 3 inches from the end of the bit. Separate the two fence posts and begin drilling on the second post, where the marks are. Once the tape reaches the hole opening, stop drilling.
Place the two posts back together. Put a washer over a lag screw and insert it into one of the openings. Screw it in using your socket wrench. Repeat the process for each screw.