Set the first beam in place, securing it at each end with 3-inch wood screws. Check the beam after it has been set to ensure that it is plumb and level. If it is not level, shim one end. If it is not plumb, twist it until it is plumb.
Attach 2-by-2 wood strips along the bottom of the first beam using 3-inch wood screws. Rip the strips from 2-by-4s or from material similar to the beam. Since the beams can be longer than the strips, miter the strips at the connecting points. Align the strips with the bottom of the first beam, and space the wood screws along the strip 16 inches.
Cut the intersecting beam to length and test fit. Cut a 2-by-2-inch notch out of the intersecting beam using a circular saw. First, mark the bottom corner of the beam 2 inches from the bottom and 2 inches from the end. Cut the notch with a hand saw to prevent over cutting the wood. Remove the notch, and use a wood chisel to remove any remaining wood chunks.
Slide the intersecting beam in place, allowing the end of the beam to intersect the prior set beam. The bottom notch should slip onto the 2-by-2 strip placed on the first beam set. Drive 3-inch wood screws through the first beam and into the end of the intersecting beam to secure the connection.
Countersink all screws, and fill the screw holes with wood filler if you would like to hide the screw heads. Sand the filler smooth after the wood filler has dried.