How can I repair my broken dining table?

I am in the process of moving and my grandmother's dining table did not fare well in the move (a dresser fell on it...). I will try to describe this as best as I can. The table top is fine, no damage done. The legs themselves are not split. But there were pieces of long wood attached to the underside of the table top they linked the legs to the top. They split (some badly). Is there a way to repair split wood reliably? Or is there a way I can attach the table legs to the table top directly without worrying about damage? I realize I could get a cheap new table, but this was my deceased grandmother's table and I spent a lot of time fixing it up before the mishap, so I'd really prefer to just save it. Thanks!How can I repair my broken dining table?
If I am understanding you correctly the pieces that you are referring to are parts of the table apron. Remove the entire apron from the table top, it should be attached with pocket screws or cleats, glue the edges of the split apron stock with wood glue and clamp firmly with several c-clamps, or large spring clamps, finally wipe off any excess glue with a damp cloth. Let the glue dry overnight and re-attach the apron to the table top. It will be as strong or stronger than it was before. Just gluing the repair while still assembled will not likely last long. To make a good repair you really need to disassemble the pieces and use clamps on the individual pieces.How can I repair my broken dining table?
You could take it to a furniture restorer. Or you could buy similar wood and try to fix it yourself.

Don't try to use the split pieces of wood. They are weak and will be unreliable.

If you fix it yourself, try to match the varnish to the table, use a good quality wood glue and screws instead of nails. Screws hold longer than nails and wood glue assures a strong repair.

Since it is an older table, the wood could be drying out. Ask a professional how to deal with this problem.
it's the chairs with my old dining room set. i got gorilla glue from the hardware store to fix them. it is really strong and should do the trick. check it out at www.gorillaglue.com. without seeing the cracks it would be hard to advise how you should go about fixing them. in most cases it is best to remove the piece and spread the crack open, wet it with water, that's what the directions call for, work the glue into the crack, and then clamp or screw it together. pre drill the holes if you are going to use the screw method. you can most likely drill these holes and place the screws so that they don't show. hope it all works out for you, good luck.
Not sure how bad the damage is, but if its mostly cosmetic, just use wood glue and glue the pieces together.

Does the leg stay on without those pieces, if so, then I would just glue them back in place, and wipe off any excess glue. This would keep it looking like it used to.

Now, if you don't care much about the piece, then you can always use wood screws and try to repair it that way.
It's hard to give you a good answer without seeing the table. I do know that they sell wood putty that hardens in the paint department of home improvement stores. It is good for smaller areas and is strong enough to hold a screw. If the splits are really long, I suggest dismantling the table legs from the split wood and cutting new wood piece to the original size. Then screw the new pieces to the original connections. Good luck!