Mark the edge of the new patio with a garden hose. Adjust the shape and size as needed, depending on how you plan to use the patio. For example, if you entertain regularly a larger patio provides extra room for your guests to mingle.
Measure the additional patio space with a tape measure. Determine the square footage by multiplying the length by the width. You will need this information when ordering the flagstone.
Dig out the grass and soil to a depth of 6 to 8 inches. Set aside some clumps of grass to fill in around the edges of the patio. Remove the excess soil to flower beds or low spots in the yard.
Add 4 inches of gravel. Spread with a rake until relatively smooth. Sprinkle with water and tamp firmly with the plate compactor.
Add 4 inches of sand and spread over the gravel. Sprinkle with water and tamp.
Arrange the flagstones on the sand. Begin along the existing patio edge, allowing a space of 1 to 2 inches between the patio and the flagstones. Add or remove sand as needed so the flagstones are level and even with the patio. Tap into place with a rubber mallet.
Pour the aggregate mix over the flagstones and sweep into the cracks and crevices. Tamp with the rubber mallet, tapping to compact and press the aggregate into the sand.
Pour sand onto the new patio. Sweep over the entire patio, filling the remaining spaces between the flagstones and gravel. Sprinkle with water and repeat as needed.
Fill in around the edges of the new patio with the reserved clumps of grass. Press into place and water thoroughly.