Before you begin to dig, lay out your tunnel plan and get a building permit from your state or local government. Building codes can vary tremendously among the states and even among cities, so be sure to finish the required paperwork, pay any fees and get required licenses in order. Also consider the water tables in your area and soil conditions. If you will be digging in an area with a high water table you may need to install a waterproof membrane in your tunnels and underground rooms. And be sure to check with utility providers, like natural gas and water, to make sure you won't be tunnelling into their systems.
Plot your course and dig your pilot tunnel. Professional tunnel diggers create a pilot tunnel, usually about one-third the diameter of the future main tunnel. This tunnel is used to verify the geology of the area and make sure your equipment and methods are appropriate. Eventually you can connect your pilot tunnel to the main project tunnel for ventilation or as an escape route, or you can widen the pilot tunnel to create your main tunnel.
Remove material from the tunnel path and underground rooms. There are several methods used to build tunnels. You can use the immersed tube method for an underwater tunnel by trenching the bottom of a waterway and reinforcing the trench with steel or reinforced concrete sections of tunnel shell. To use the cut-and-cover method of tunnelling, dig a trench big enough to contain the tunnel and it's concrete shell. You can use a box like tube of concrete to reinforce walls as you dig. Cover the tunnel with the previously excavated dirt. The top-down method of tunnel construction requires a parallel pair of walls embedded into the ground along the proposed tunnel route. Dig your trench between the walls, but not all the way to the bottom of them. Create the tunnel roof by framing and pouring reinforced concrete on the bottom of the trench. Then use excavating machinery like a front-end loader, to dig underneath your cement tunnel roof. Finish by pouring a concrete floor.
Dig your underground rooms. Underground rooms, like basements, are usually created using heavy equipment like track hoes. Begin by digging the hole. Then spread gravel around the sub-rough plumbing if you will be plumbed. This gravel will sit under the cement pad which will become the floor of the room. Lastly, backfill and do a final grading, before pouring the cement floor.
Digging tunnels and underground rooms can be extremely dangerous to both humans and the environment. Do not dig unless you have permission from your local government.