Design the total size and shape of your stage. Divide the design into 4-by-4 foot sections. Parcel smaller areas into 2-by-4, 2-by-2, and so on. For example, if you need an 11-by-8 foot stage, you will build six platforms. Four will be 4-by-4 and two will be 3-by-4. You could build 4-by-8 platforms, but they are very heavy and not as transportable.
Cut your 3/4-inch plywood to the sizes you require. Plywood in 4-by-8 sheets is cheaper, but 4-by-4 sheets are easier to carry and can save labor with fewer required cuts.
Build a box frame for each plywood sheet, following the outside dimension. The plywood should be flush or just shy of the edge with no overhang. Lay out 2-by-6 inch stud lumber on a level surface with the boards standing taller when looking from the side. Studs flex too much if used the other way.
Attach the studs to each other with three 2-1/2 inch decking screws or nails at each contact point by driving through one stud into the end of another, forming a butt joint. Glue joints with construction adhesive to minimize creaking.
Join more studs so the plywood never goes 24 inches without support. A finished 4-by-4 frame will have two parallel 48-inch boards attached to two slightly shorter studs to make a square; the shorter measurement accounts for the width of the two long boards. A third stud should bisect the middle and butt to the shorter studs to insure the fasteners run in multiple directions.
Use a caulking gun to apply construction adhesive to the top of the studs in a wave pattern. Lay the plywood on top of the box frame and attach with 2-inch deck screws, nails, or staples. Try to center all your fasteners in the stud. For a less permanent platform, skip the adhesive, but your finished product will be noisier.
Attach 2-by-6 lumber inside the four corners as legs to add height to the platform. For most applications, cut the legs equal lengths and use shims to level the deck. Attach the legs with carriage bolts for more strength and ease of take down and reassembly. If using screws, drive from the frame to the legs, not the other way.
Screw, bolt, or clamp the platforms to each other to create a stable system. Take special care to make the platforms flush to each other. The surface of the stage platform should be smooth, without gaps or lips that can trip performers.
Erect the stage platform and paint the top and visible sides for a single event. If the stage will be moved and rebuilt, paint each platform prior to assembly. Provide a blueprint for stage construction by labeling underneath the sections.