Place a blanket or towel on the floor of your work area. Putting one on the floor before flipping the table will protect the tabletop from scratches.
Flip the table, without legs, onto its back. You should see the four sections, or L-shaped brackets or openings, where the legs are screwed in.
Place one of the legs in the proper position. If the leg is the same shape on all four sides, there shouldn't be any problem fitting it in. There should be one or two long machine screws--usually about 2 inches long--attached to the leg, on one of the sides. The side with the screws should face toward the middle of the table. The screws should be closest to the upside-down table top.
Place the washer on the screw, followed by the nut. Twist the nut, by hand, until it's tight against the washer. If desired, tighten the wing nut with a wrench. Repeat for the other three legs.
Test the legs by trying to "wobble" each one. If the leg doesn't move, it's secure. If it does, tighten the nut with a wrench. Flip the table back over.