You’ll have to replace the top or re-skin it. If the frame is still good; cut, shave, chop, sand, plane or what-have-you the parts sticking up above the normal level. Don’t worry about making gouges or holes in the surface. If surface is mostly intact, skip the second paragraph. Intact means still structurally sound, doesn’t have huge holes or gouges say 6" or more across. New panels will take care of most irregularities if the high spots are gone.
If surface is very irregular - fill in all the dents, cuts, crevice, and holes with autobody filler or drywall compound. Let dry. For large holes through that could affect stability, put the table face down on a flat surface (driveway, garage floor) and glue a flat piece of plywood over the hole (weight down with something to increase holding power). When set, turn table right side up and fill the hole; the plywood now acting as the bottom.
Measure the top (fold up with two pieces??) and get replacements at your home center. Plywood with one “A” side; 3/8" or thicker if table needs some stability. Also 1/4" “hardboard” (not perfboard though that would make things interesting) can be used if the table frame is good. The home center will make the cuts for a nominal fee or free to fit in your car. Get some panel adhesive (liquid nails or similiar - store can recommend). Paint, white and usually green. Store will recommend. You just need small amounts. Spray cans, if you can stand the smell, work after a primer coat.
Make sure your replacement top is the correct size. Sand or scrape down any high spots in the filler which is now dry. Doesn’t, in fact shouldn’t, be mirror smooth. Apply beads of adhesive near the edges and across the in between areas in long beads (lines). Put the panels down aligned with the edges of the table frame. Slide around a little bit if possible, this spreads out the adhesive some. When in final place, weight down the top all over with books, cement blocks, anything with wide flat surfaces, to strengthen the adhesive bond. Let dry (directions on tube) then paint.
Materials and tools:
Sander, scraper, plane, etc… something to cut or wear off the high spots. Borrow from neighbor if possible.
Putty knife, 3-5" to spread the drywall or autobody filler around. (if top is in bad shape)
Drywall compound, if needed, small, store can determine. You can use around the house for nail holes in wall, gouges from chairs, etc…
Panels from home center - cut to fit frame.
Panel adhesive from home center - one or two tubes - store can determine.
Paint, white and whatever color you want the table top - green usually. Gloss or semi-gloss.
Masking tape.
How to paint. (Important - keep cat off wet paint:):)) White on everything first - acts as a primer coat. Just get in on there - no artistry required. Put a second coat around the edges and down the center line. Mask off with the tape where the lines will be, paint the rest of the top green or whatever. Pull off tape when main coat is just starting to set (you don’t want the main color to leak on to the white (too wet) or pull up the main color (too dry). When everything is set, put up net and enjoy.
It will take an entire weekend if you have to fill holes but 90% of the time is just watching filler/paint dry so it’s not like a full time job.
If plywood has gaps around edges, fill with the drywall compound/autobody filler, sand down, and paint white.