Checking it's square while the glue is still wet
By the time the glue's on and your screws or nails are going in or already in, you're maybe five minutes from wanting to walk away and let the clamps do their work overnight. Don't walk away yet. This is the step people skip, and it's the one that actually decides whether your shelf looks right on the wall or looks a little off in a way you can't quite name.
Square. We're checking square.
Why this matters more than it seems like it should
A shelf can be perfectly cut, perfectly glued, perfectly clamped, and still end up leaning like it's tired if the corners aren't at 90 degrees. Wood doesn't fight you much once it's dry. Glue sets, screws hold, and whatever shape it's in when it sets is the shape it keeps. So the window to fix it is right now, while everything's still a little movable.
People tend to think of squareness as a finishing touch, something you check at the end when it's already too late to do anything about it. It isn't. It's a during-the-glue-up thing. That's the whole lesson.
How to actually check it
You've got a couple options and I'd use more than one.
The square, if you have one. Set it into the corner of your shelf frame, against the two inside edges. Any gap along either arm of the square means that corner's not square. This is the fast way and the one I use most, mostly because Mary got me a decent one for my birthday years ago and it's still the tool that changed the most for me. Before that I was eyeballing corners and wondering why nothing lined up right when I went to hang things. A cheap combination square from the hardware store works fine for this. You don't need anything fancy.
The diagonal measurement, if you don't have a square handy or you want a second check. Measure corner to corner, one diagonal, then the other. If your shelf is a rectangle and it's square, those two numbers match. If one diagonal comes out longer, the frame's leaning toward a parallelogram, which is a fancy way of saying it's racked over to one side. The bigger the gap between the two measurements, the worse the lean.
I like doing both. The square tells you a single corner is right; the diagonals tell you the whole frame agrees with itself. Do the diagonal check especially if your shelf has more than four corners, more than one shelf level, that kind of thing. A square in one corner is no guarantee the opposite corner is behaving.
If it's off
Here's where the wet glue is your friend. If your diagonals don't match, you can usually nudge the frame back into square by pushing gently on the corners of the longer diagonal, squeezing it slightly, while the clamps are still loose enough to allow movement. Recheck. Adjust the clamps once it's sitting right. Don't crank everything down first and then try to wrestle it square after, you'll fight the clamps the whole time.
If you're assembling on a flat surface, like a workbench or the garage floor, that flatness is doing a lot of the squaring work for you already, so lean into it. Set the frame down, get your diagonals close, and let the flat surface hold it while you finish clamping.
One thing I'll say plainly: don't rush this because you're excited to see the shelf take shape. That's just when people skip it, they're so close to done that squaring feels like an unnecessary pause. It isn't. Five more minutes now against a shelf that's permanently a little crooked. Take the five minutes.
The tall mistake
I built a step stool for Mary a while back so she could reach the top shelf in the kitchen, and I got so wrapped up in getting the legs even and the whole thing square and solid that I never stopped to think hard enough about the actual height she needed. It came out square. It came out sturdy. It also came out a little too tall to be genuinely useful as a step stool, which is its whole job. She uses it as a plant stand now. Calls it "the tall mistake."
I bring it up here because square isn't the same thing as right. You can get every corner checked and every diagonal matching and still have missed something upstream, a measurement, a piece of layout, a size decision. Squaring what's in front of you is necessary but it isn't the whole job. Keep an eye on the bigger picture while you're doing the small careful checks. Both at once. It's a lot to hold, I know.
A quick caution
If you're pushing on a frame to square it while the glue's still workable, do it with steady, even pressure, not a sudden shove. Wet glue joints aren't at full strength yet, and a hard yank can pop a joint apart rather than nudge it into line. Gentle and patient wins here.
Before next time
Let it sit clamped overnight once you've got it square, and don't peek at it every twenty minutes out of nerves. Check it once more before bed if you want, just to be sure nothing shifted, then leave it alone.