Long edge joints like with slabs, first thing is you want the wood to be dry, or about as low a moisture content as your area will allow. There's kiln and natural air drying. I think preferences and some disadvantages with both ways, but that's a slightly different topic than edge gluing, so just be sure you are dealing with seasoned wood. Otherwise, no matter how good a joint you have, as the wood needs to much continue to dry, it will split at the ends where the joint is. A shame to have a nice tight joint that opens up. With not properly dried wood, end checking can be prevalent as well.
Edge jointing so there is a minimal glue line and for strength so it doesn't pop apart, requires both edges to be really flat with no high spots between the ends, whether you do that on a jointer, tablesaw, or planing by hand. High spots between the ends increase the tendency for the joint to open up. Glues are strong nowadays, but no glue is stronger than thick wood that wants to pull apart. Slightly sprung so the wood has a very slight gap in the middle decreasing outwards, and is full sitting on the very ends is actually the ideal, because when you clamp it together, it pulls the ends even tighter together which adds some strength there, the most vulnerable point of failure from wood movement.
After your jointing method, place the edges together sitting up on one outside edge on your bench. You can check for high spots by gently pivoting the top board on the lower one and it will tell you how the wood edges are meeting. Do that from both ends, and you can exert slight hand pressure at the top middle of the top board to steady things and not have the top board fall off. You can also check for rocking to see if where the wood is sitting faces are all meeting evenly. Ideally the edges should be stable with no rock, but invariably you will get a little or a lot of that with long glue ups, because either your jointing method was faulty, or one or both boards have some twist in them. When there is twist and the meeting faces rock, when you pull everything together the unevenness will twist the surface out of being plane. You can use a little rocking to you advantage though, because if there is twist, some rocking in the opposite way from the twist will correct the twist over the entire wide surface when you glue together. It's a somewhat advanced technique, but it does save the trouble of taking twist out of a glued up wide surface with a plane or sander. That's not a problem if the degree of discrepancy from flat is minimal and you have the wood thickness to work with, but twist as reflected from where edges meet can really make for cupping and reverse on the other side when you get the whole thing glued up. You'll end up having to take off a lot of wood all around to make flat and end up with the same thickness everywhere. Also, when you have the boards sitting together up on edge, take a long straight edge and make sure the top board isn't leaning away to one side or another from the lower one, or you will have to correct that by affecting an edge to bring things back up to square before gluing up. That happens when there is twist in the boards and they meet at the edge, things get whacked out. Precise machining in woodwork really makes life easier, if set up to do it.
Woodworking is a multi-stage process, and the secret to coming out with a well done thing at the end, is having each step along the way done with as much exactitude as you can. Problems progressively accumulate if you don't. If the outside edges of the boards are natural edges like on Steve's nice table, obviously you can't check how the glue edges will meet by having the boards sitting up together on your bench, so you'll have to figure it out by laying flat, a bit harder to see and determine, or jury rig something up so the lower board can sit up on it's outside edge and you can place the other board on top of it. Whatever you do, make sure the ends touch solid with no gap there. Three board or more glue ups are exactly the same process per each meeting board edge, whether you do it and glue up in stages, or glue the whole thing together at the same time. If you get each edge flat and true, the whole surface will be when put together, or close to it.
When you do get to gluing up slabs or whatever where it's a long joint, alternate your clamps from one side to another to try and keep the surface flat, Check with a straight edge over the width at various points, If the surface isn't flat at various points, make up some large wooden wedges with a sharp leading edge, and bang them under the clamp bar at the joints at the convex side of the irregularity, and it will push the surface up to being flat how you want it until the glue dries. Verify with a straight edge. That's a simple but cool trick that not many know.
Biscuit joiners are really great for holding together edge joints, and for giving alignment when gluing up. Indispensable really if you are doing a lot of it. The old way was using dowels or having a spline, but the biscuit method is very quick and easy.
If some or all
of this is confusing, I'll be happy to try and clarify. Oh yeah, make sure you get everything pulled up tight and out of sight before the glue sets up, or it's crying time.