Fold a piece of sandpaper in half and run it back and forth along the split, you'll sand both sides at once and save yourself some time, plus you'll be sure you've sanded evenly so the repair will hold tight together.
Apply a good quality wood glue to the sanded wood making sure to cover all exposed wood.
Use a couple of nice bar clamps to hold the repair, and space them so that the table is getting equal pressure along the split.
If your piece is a softer wood, you'll want to put a buffer between the wood and the clamp to protect it from getting damaged.
Once you've tightened the clamp, you'll more than likely have some glue squeezing out along the seam. Use a damp cloth to wipe away any excess glue so that it doesn't mar the surface of the table.
Allow the repair to dry and remove the clamps. To add moisture to your wood furniture use some mineral oil on a soft cloth every month or so. I'm Mrs. Fixit and it's just that simple.