A wobbly table or chair is almost always loose screws, failed glue joints, or uneven legs. Most fixes take under 15 minutes.
Turn the table or chair upside down. Tighten every fastener — leg bolts, cross brace screws, corner blocks. Work around the piece systematically.
If any joints feel loose or move when you push on them, clean out old glue from the joint surfaces. Apply a thin coat of wood glue to both surfaces, push together firmly, and clamp. Let cure for at least two hours.
Flip it back upright and set it on a flat surface. Rock it to find which leg is short. Stick a self-adhesive felt pad or furniture shim under the short leg. Add more until it sits completely stable.