To 'fix' it, you should remove any 'crud' in the opened joint/crack (cause almost no adhesive will work well with 'crud' in the way) and then use an adhesive to 'glue' the joint back together and clamp it all up until the adhesive sets and bonds (overnight in the clamps is usually more than plenty for a non-stressed joint, usual recommendation is 24 hours minimum in the clamps for a 'stresssed' joint).
All that assumes that the original joint configuration was 'correct' (decently flat faces of the wood edges being glued together and no big gaps or such).
Obviously, to glue the crack back together you have to get the 'glue' down into the joint. Sometimes you will want to spread the crack open at least slightly (get your mind out of the gutter there

) in order to ensure you can get the adhesive down into the joint.
Titebond is a pretty big name in wood glue. Titebond is 'the' (or one of the) original 'yellow woodworking glues'. Works nice, when used appropriately. Titebond II is a water-resistant (when dry/cured) yellow woodworking glue. Titebond III is another water-resistant (when dry/cured) yellow woodworking glue.
http://titebond.com/woodworking_glues.aspx
Used 'properly', all of the Titebond woodworking glues typically make a joint that is stronger than the wood itself (the wood will rip its own fibers apart apart before the glue lets go!)
Another 'common' choice for 'gluing' something together may be an epoxy (single quotes used because epoxy is an "adhesive" and not a "glue", technically). Epoxies come in many many different 'flavors' or formulas, so RTFM and use the appropriate product for the task.
When clamping the wood together, do
NOT crank the clamp(s) so tight that all the 'glue' is squeezed out of the joint!
No 'glue' in the joint = nothing to hold the joint together
Tighten the clamps just tight enough that there is just a thin even line of 'glue' in betweeen the pieces of wood being joined (about the width of a pencil line is usually good there) and just a little bit of 'glue' gets squeezed out of the joint to the surface (no squeeze-out and you either have the joint still too 'loose' or not enough glue in the joint in the first place).
Glue dripping all over the place means you are making a mess and wasting glue.
Of course you could go all-out and rip (cut apart, not 'peel' apart) the joint apart, plane or joint the edges as needed, and then glue it all back together.
Although a 'properly' made joint in wood using modern adhesives is usually stronger than the wood itself, you might want to mechanically pull the wood strips together with a cleat (underneath the top as mentioned above) or you can drill through the side of the top and then put a piece of threaded rod through the new hole and clamp the top all together that way. Usually not needed though.
