Measure the site for the extension, using a tape measure. Lay a rope down to mark the outside edge of the extension.
Remove the soil from the area between the rope and existing driveway, using a shovel. Dig until you've removed approximately 1 foot of soil. Tamp along the bottom of the hole with a tamping tool to stabilize the ground.
Fill the foundation with gravel, and tamp it down until the base is 8 inches thick.
Line the inner walls with 2-inch by 4-inch form boards along the outside perimeter of the foundation. Use a bubble level on top of the form boards, and adjust the boards to match the slope of the existing driveway so water will run away from the home. Nail the boards together with a hammer.
Place an expansion joint vertically between the outer edge of the existing driveway and the inner wall of the foundation. Premolded from rubber, cork, foam, fiber or other materials, the expansion joint should be 1/4 inch to 1/2 inch thick. The joint will absorb tension between the new and old cement, preventing the driveway from cracking.
Mix the cement with premade mix and water in a wheelbarrow, using a paddle bit and drill.
Pour the cement and spread it into corners with a gauge rake, and then drag a wooden board across the top of the forms to push the excess into low areas. Cover the wet cement with damp, breathable material such as canvas and slow-dry the extension for about seven days.
Remove the form boards from the hardened cement, using a flat pry bar, and fill in any gaps around the outer edge with soil.