Remove the fascia and railing members from the side of the deck that you're expanding with a pry bar and framing hammer. Measure away from the existing beam's ends and use marking paint to lay out the corners of the addition on the ground at the desired length.
Pound stakes into the ground roughly 18 inches from the outer side and end of the desired location of the post footings' centers. Locate the footings along the side of the addition's perimeter that's not adjacent to the existing deck; one at each corner of the addition's perimeter and evenly spaced between. Consult a beam span table, available at a lumberyard or your local building authority, to determine the required spacing between footings. Spacing ranges from 4 feet to 8 feet or more, depending on soil conditions and project-specific design characteristics, such as beam size and load capacity.
Run some string line between the opposite side stakes and between the end stakes and the beam's top edge to form a a three-sided string form. The pieces of string should overlap above the center of the proposed location of the post footing. Align a builder's square at the strings' intersections to check the strings for square. Alternatively, use the Pythagorean theorem (the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides), also called the 3-4-5 method, to check for square.
Align a builder's square at the strings' intersections to check the strings for square. Attach a line level to each string, check for level and adjust as necessary. Use a shovel to dig a footing hole below the intersection of the strings; plunge the shovel into the ground, tilt and lift the soil from beneath the strings. Size the hole according to local regulations and the requirements of your tube form. In general, footing holes are twice the diameter of the tube form and equal in depth to the tube form's height minus the required protrusion above grade. Depending on local regulations, footings must protrude several inches or more above the ground's surface.
Set tube forms in the holes. Align the forms with the strings' intersections and check the tops of the forms for level. Fill the bottom of the forms with several inches of gravel, as required by the form's manufacturer and local regulations. Fill the space between the trench's side and the form with gravel. Compact the gravel manually or with a tamper. Fill the forms with premixed concrete and the set post base brackets at the forms' tops. Align and level the brackets according to your design; if a beam will rest in the brackets, ensure that it's level with the existing deck's beam.
Allow the footings to cure. Measure, mark and cut post and beam lumber to size with a circular saw. Most projects call for 4-by-4 posts and 4-by-6 beams. However, precise sizing depends on project-specific design characteristics, such as deck loads and height. Refer to a beam span table to determine exact requirements. For low-lying decks where the footings rise to the level of the existing deck's beam, you won't require posts.
Set the posts or beam in the footings' brackets and fasten the lumber to the bracket with framing nails or the bracket manufacturer's suggested fasteners. If your installation requires both posts and a beam, install beam saddles atop the posts. Place the saddles on top of the posts, align the saddles' lower "legs" with the sides of the posts and fasten the saddles to the posts through their bolt holes with framing nails, lag screws or the saddle manufacturer's suggested fasteners. Set the beams in the saddles. Level and plumb the post and beam members before driving in the fasteners.
Measure, mark and cut joist lumber to span from the existing deck's beam to the newly installed beam. Joist size depends on the distance that the joists must span and the loads that the joists will bear, such as the weight of decking materials, snow, people or hot tubs. Available at building departments and lumberyards, charts called joist span tables outline allowable joist spans, spacing and lumber sizing. Mark joist locations on the new beam, following the spacing of the existing deck. The new joists will butt against the sides of the existing joists; accommodate this arrangement by offsetting your layout marks to one side of each existing joist. Set one end of the joists atop the existing beam and align the other end with the layout marks atop the new beam.
Toenail and face nail the new joists to the existing beam and the side the existing joists. Toenail the new joists to the top edge of the new beam, using two nails per joist. Fasten some blocking -- constructed of joist lumber -- to the outer faces of the new side joists to create a surface that's flush with the outer face of the existing joists and provide a nailing surface for deck planks and side fascia. The new and old joists are arranged side by side; blocking or furring strips fill the gap between the joists on the addition's sides, allowing you to attach deck trim if desired.
Measure the deck from side to side, perpendicular to the joists' length. This dimension represents the deck planks' length. Add the desired amount of overhang to the length; if you're installing trim, the overhang equals the thickness of trim on both sides of the deck. Cut planks to size with a circular saw and lay them perpendicular atop the joists and fasten them with deck nails or screws. Drive at least two nails through the planks at each joist. Cut and fasten the planks to the joists and complete the deck surface.