If the melamime is square edged it is quite simple to glue a new surface over the old. If you have a rounded edge, you could consider getting a GRP specialist to do a gelcoat match into the damaged area.
I made some kitchen cupboards with melamine board some time ago. It is a bugger to cut, and blunts anything very quickly. I cut it using a circular saw, which chipped the edges. I then then ran a router along both edges (i.e., top and bottom) to get the final size and a smooth edge.
I don't think you can buy melaime in thin sheets. However, there are other products that you can (e.g., Laminex). You could stick a sheet of such material onto the existing surface.
I used a router to make bull nosed timber edges that I stuck to the top of the kitchen bech (on which I had glued Laminex).
Dont bother. Rip it off and put back a nice piece of veneer. Easy to cut n stick and after a couple of coats of varnish looks a lot better imho of course. /forums/images/graemlins/smile.gif
Are referring to formica or melamine here? Melamine is soft and is the kind of product used to cover chip board on cheap sets of household drawers etc. Formica, or equivelant is hard, brittle plastic that is very hard to repair once broken and will be hard to remove. My galley has formica topped surfaces and I would replace the formica if became damaged rather try to repair.
Melamine is a hard decorative laminate of which Formica is a branded version. You can cut melamine or Formica with a circular saw, sabre saw or you can get a laminate blade for a Stanley knife. If you use the knife you score the top surface and then bend the material and it will snap along the cut line. If your melamine top runs all the way to the edges of the table I would glue a new sheet over the old. Cut the sheet slightly oversize to allow for trimming which you can do with a Surform tool. If the laminate is rebated into a wooden table leaving a border, as was the case with my tables, you will have to remove the old laminate, which is a pain. A chisel and a lot of patience is required.
You also used to be able to get a scraper tool which would follow the edge of the underlying woodwork, curves and all, and neatly trim the laminate with a bevelled edge which needed no further work.
I think I've still got one in the garage. pm me if you're stuck.