Plan a route for the underground wiring. Keep the number of bends or angles in the route to a minimum. Avoid having more than 360 degrees of bends in the route, which would violate the National Electrical Code.
Check with your local building department to obtain a permit for your work. Call 811 to have your underground utilities wires marked.
Select a location for where the new wiring will leave the house. Pick a spot near the circuit breaker at the bottom of a wall, or the top of a basement wall. Take a reciprocating saw and cut out a small section of drywall. Make shallow cuts to ensure that you do not cut into any wires.
Remove the drywall. Drill a 1-inch hole at this spot through the wood and siding. Center a junction box over the hole on the house's exterior and screw it to the wood.
Dig a 24-inch deep trench about the width of a shovel along the length of your route with a mattock. Ensure that the trench is 24 inches deep, the minimum depth for underground cable not protected by conduit.
Lay the UF cable in the ground along the length of the trench.
Measure from the junction box to the hole on the outside of the siding. Place an appropriate size length of electric metallic tubing, or EMT, into the box using a conduit connector. Use another conduit connector to join the EMT to the LB fitting, which allows for a 90-degree turn.
Take a curved piece of EMT, called a conduit sweep bend, and place it at the bottom of the trench directly under the LB. Measure from the LB to the conduit sweep bend. Cut a piece of EMT conduit to that length and use it to connect the LB fitting and the bend.
Fasten the LB to the house with a steel conduit strap and masonry screw.
Feed the UF cable up through the sweep bend and into the junction box.
Go to the other end of the run and drill a hole for the shed junction box. Screw the box to the wood exterior. Make the conduit connections and feed the cable into the junction box in the same way you did for the house junction box.
Hire an electrician make the final connection between the house junction box and the new dedicated line at the circuit breaker. Call the local building department to make a final inspection.