Rub a folded piece of sandpaper along the split to remove rough edges and form a smooth bonding surface. Use medium grit for very rough edges and fine grit to smooth.
Spread a high-quality wood glue in the split, making sure to cover the crack thoroughly over its whole length.
Place a bar clamp across the table. Use more than one clamp for a large split, making sure to space them so that there is even pressure distributed along the split. Put a folded dishtowel or another kind of padding between the end of the clamp and the table to prevent damage to the table.
Tighten the clamp until the split is forced together. Start with the center clamp first if using more than one clamp.
Wipe off any wood glue that oozes out of the crack with a damp cloth.
Allow the glue to thoroughly dry, and then remove the clamps.
Apply lemon oil over the repair if it is not really noticeable, or touch up the repair with stain, and varnish the entire table.