Extending an existing concrete patio with concrete or brick pavers involves the same basic process as building a new patio. The key difference is that the new portion of an extended patio must be perfectly flush with the old patio. For most applications, the best way to build the new surface is by setting the pavers in sand (called sand-set installation). Sand-setting is easier than mortaring, which requires a concrete slab as a base, and allows you to fine-tune the level of the new surface simply by adjusting the sand bed before setting the pavers.
Establish layout lines for the new patio using stakes and mason's string. If the old patio is sloped for water drainage, the new patio should be sloped in the same way; adjust the level of the layout strings to follow the same slope -- a slope of 6 mm (1/8 inch) per 30 cm (1 foot) is typical. Plan to install the pavers so that they're touching the edge of the slab.
Excavate the ground to a depth that allows for a 10 to 15 cm (4 to 6 inch) gravel subbase, a 5 cm (2 inch) layer of sand, and the thickness of the pavers. Extend the excavation area about 15 cm (6 inches) beyond the finished patio on all sides (except the slab side). Measure down from your layout lines to gauge the depth of the excavation.
Fill the site with a 5 to 7.5 cm (2 to 3 inch) layer of compactible gravel. Rake the gravel flat and tamp it with a rented plate compactor. Add 5 to 7.5 cm (2 to 3 inches) more gravel and tamp again. If desired, you can cover the gravel with landscape fabric to further inhibit weed growth from the soil below.
Add 5 cm (2 inches) of bedding sand and screed it (smooth and level it) with a long, straight 5 by 10 cm (2 by 4 inch) or 5 by 15 cm (2 by 6 inch) board. Test-fit a few pavers along the edge of the old patio to make sure the pavers will be level with the surface of the concrete.
Begin setting pavers along the concrete edge, using the desired pattern. Set the first few courses of pavers, then use a straightedge or level to make sure the pavers are level with one another and with the old patio. Continue setting pavers to the opposite edge of the patio. Install patio edging along one or more sides of the new patio, as desired.
Spread fine mason's sand over the pavers, then sweep the sand across the surface to fill the joints between pavers, locking them in place. Dampen the patio with water from a garden hose, and let the area dry. Repeat until the paver joints are filled and the sand in the joints is firmly settled.
Some concrete paver manufacturers recommend tamping the pavers with a plate compactor to help settle the pavers and sand; check with the manufacturer or retailer for detailed instructions. Paver styles vary greatly; choose pavers that complement the existing concrete surface.