Support the larger, taller beam on top of a metal column according to the builder's plans. Beams will rest on a post or in a notch in the foundation to transfer the weight of the building to the foundation.
Place the second, shorter beam on the same post. Make sure the ends of the two beams are flush, and no empty space is left between the two.
Raise the shorter beam using 1/4-inch metal shims until the two beams are level across the top surfaces. Stack the shims on each other, under the shorter beam. These shims should be metal, not wood, so that they do not compress over time.
Splice the two beams together using metal truss plates or splice plates. The truss plates lie along both sides of the beams and prevent lateral twisting. Nail-on truss plates can be used for smaller, single member beams. Larger beams, laminated beams, or beams made of multiple pieces of dimension lumber should be bolted together with splice plates.
Hold the splice plate along side of the beam and mark the holes on the wood. Drill 1/2-inch holes through the beam with the auger bit. Insert the bolt through the plate, and then hammer the bolt through hole in the beam. Slide the truss plate onto the bolts on the other side of the beams, and then bolt the two together, sandwiched between the truss plates.
Mark the placement of the smaller beams along the larger main beam. Layout the exact placement so a metal connector can be used to mount the smaller beam.
Attach a properly sized joist hanger to the side of the main beam. Smaller, lightweight steel joist hangers are attached to the main beam with truss or sinker nails. Larger steel plate hangers are mounted to the main beam by bolting them with 1/2-inch carriage bolts passing all the way through the main beam. Do not use lag screws or all-purpose screws to attach joist hangers to a main beam. Mount the hanger so that when the smaller beam is inserted, the top surfaces of the beam are flush.
Insert the smaller beam into the hanger. The beam must be supported on each end at this point, so that the smaller beam is flush with the main beam.
Nail or bolt the smaller beam in place with the same fasteners used to attach the metal hanger to the main beam. Small beams can be nailed into place. Laminated beams should be bolted into place using bolts passing all the way though the material.