When edge joining boards to, say, make a panel or tabletop I always use cauls positioned crosswise to the length of the boards. Here's my procedure.
Lay two cauls on the work surface in the same direction that the boards to be joined run. The purpose of the two cauls is only to raise up the other cauls and workpieces from the work surface so that it is easier to position clamps. My cauls are about an inch thick, a little less than two inches wide and about 30 inches long. The top surface of each caul should have a coating of tape so that when it comes in contact with the workpiece and the glue joining the workpieces the caul will not be glued to it as well.
Lay cauls crosswise to the base cauls positioned in Step 1. Stand a clamp upright vertically next to each caul. Because I was given a lot of clamps in addition to the clamps I purchased originally (you know, you can never have too many clamps), I space the cauls about 6 inches apart. Probably every 12 inches would work just as well. The wider the individual boards being joined then the fewer clamps needed because of the pressure angle coverage you get.
Lay the workpieces to be joined show face up and perpendicular to the cauls in Step 2. For purposes of this description, say you are edge joining five pieces to make a wide tabletop panel.
Begin to apply glue to the edges of the workpieces. Turn up the two boards that will be joined at the far side of the panel so that the edges to be glued are in the "up" position. Apply glue to these two edges. I squeeze glue from a smaller bottle along the edge and then use a small roller to distribute the glue. You want all surfaces fully covered with a light covering of glue.
Edge join the two glue surfaces, slide the edges back and forth against each other a couple of times to be sure the glue grabs tightly.
Repeat Steps 4 and 5 for the two boards that will be joined at the near side of the panel.
Take the middle board, the 5th board, and apply a more generous amount of glue to both of its edges. Repeat Step 5 by positioning the middle board between the other two sub-assemblies.
Lay cauls across the top of the assembly. Position each caul so that it lines up with and is parallel to a caul on the underside of the panel. Position the clamp head of the short clamps just over the edge of the assembly to grip the two cauls and workpiece and lightly tighten it. Do this for all of the cauls. If you are using 5 pairs of cauls then you will be using 10 clamps.
At the ends of the workpieces, use small clamps positioned vertically to lightly grip the edge joints between two boards to hold the faces of the boards flat.
Now with clamps long enough to span the horizontal width of the assembly, apply clamps to the long edges of the workpieces to draw the edges of the boards together but just lightly tighten the clamps. I position the middle clamp on top of the assembly, then the clamps on either side of the middle one are positioned on the underside of the assembly. The next pair of clamps are again positioned on top. By alternating the clamps this way you even out the pressures to help keep the face of the panel flat instead of bowing it. With your finger, check the edge joints to make sure that the edges of the boards being joined are flat against each other. If not try to bring them into alignment.
Now firmly tighten the vertical clamps that grip the cauls and firmly tighten the vertical clamps on the ends.
Finally, begin to firmly tighten the long horizontal clamps to bring the workpiece edges tightly together. As much as possible keep checking the long edges to make sure that the boards stay flat to each other and that no edges are raised above or below the adjoining edges. The more clamps you use the more difficult it is to have enough space to easily turn the handles.
Let the glued assembly remain in the clamps for about an hour.
Remove clamps and immediately scrape all joined edges to remove glue squeeze out. If there is no squeeze-out you may not have used enough glue but don't cry over spilled milk since there's nothing you can do about it now. If you have a mild amount of squeeze-out you're right on the money. If you have a lot of squeeze-out, then you know you can use less the next time around.
If some edges are raised from the adjoining edges then the panel will have to be flattened. If is is narrow enough, that can be done in the thickness planer. If it is too wide for the thickness planer then you will have to use a hand plane, card scraper or sand the surface flat. By using lots of cauls clamps as described I've been very successful with keeping flat all of the panels and tabletops I've made recently. Good luck on yours.
Larry Martin