Determine where you want your mailbox to end up. Take pictures of your mailbox's current location and where you hope to move it, as well as pictures of your entire front yard.
Take the pictures to your local post office and tell them about your plans. Ask them if your plans meet their regulations and, if possible, speak with your carrier to make sure he doesn't have a problem getting to your mailbox at its new location.
Use the shovel to dig up the area all around your mailbox post. If your mailbox is held up by a concrete slab, use a chisel and hammer to break up the concrete and then use the shovel to move the concrete pieces back and forth until they come loose from the dirt and can be removed.
Loosen up the ground around the post as much as possible, then pull the post out of the ground by sliding it free with a few gentle tugs.
Fill the hole where the mailbox used to be with the loose dirt. If you have concrete pieces, clear them out and source extra dirt or sand from another area in your yard to fill the hole.
Use your shovel to dig a hole 1 foot deep and about three times the diameter of your post. Flatten out the bottom of the hole and use the level to ensure that your post will stand straight up on level ground.
Have someone hold the mailbox in place in the new hole. Use your shovel to refill the hole with dirt. Use your level to pack the dirt down as you go to give your post more stability.
Top off the area around your mailbox post with dirt or sand (if you need extra, get it from your own yard to save money) and, again, use the level to pack it down.