Lay down a furniture pad and place the table on it so the table's underside is facing upwards. The furniture pad protects the table top from getting scratched.
Position a steel bracket that's close to the table in length in the middle of the table top's underside. The bracket supports the plywood so it won't bend.
Drill screws into the bracket to hold it to the underside of the table. Make sure the screws are short enough to not penetrate the table on the opposite side. The brackets usually have predrilled screw holes, so put one screw in each. Otherwise, insert a screw every 6 to 8 inches to ensure the bracket is fully supported.
Add more brackets as needed until the table top doesn't flex at all when weight or force is applied to it.