I don't know how far you are along so I'll just offer some general guidance. I've made a lot of sawdust in my time, and this can be something really frustrating.
1. Make sure all your right angle cuts are exactly 90 degrees.
2. Make sure all your right angle cuts are exactly 90 degrees.
3. Make sure your table saw, saw fence, and everything about it is perfectly calibrated. Measure all the angles with a good L-square ruler. This way all your right angle cuts are exactly 90 degrees.
4. Measure, measure, measure. If you use a table saw, cut pieces that are supposed to be the same length all at the same time, that way you don't have to adjust the stops.
5. 45 degree cuts are sometimes the hardest. If you're of by even .1 degrees, it won't make a precise 90 degree angle. I have a jig whereby I can shave off the ends to make them precisely 45 degrees, and then I have an L-clamp that holds both pieces at exactly 90 degrees while they're glued/tenoned/pinned together. I prefer biscuit joints here, but tenons can make a very strong joint and they can look very artistic as well.
Okay, enough measuring tips, but I can't stress how important that part of it is.
6. When gluing 90 degree pieces together, get some L shaped clamping blocks:
Four or eight of these clamps should do the trick to make any box square while the glue sets.
7. Wood warps, and this is the enemy. Check key structure pieces for warp by placing them on a nice FLAT surface (surface of a table saw is real good for this). Sometimes the wood will develop a warp after you've cut it. Softer woods like pine and fir can be forced back, but they'll just put strain on the rest of the piece you're making and it will pull itself apart over time. Hard woods like oak or maple just won't cooperate. I've had to re-cut pieces because they developed a warp. Sometimes a nice Delta planer can make it flat again, but I don't own a nice Delta planer.
A good measuring tool.
Another good measuring tool.
I'm kind of a tool freak.
I have an entire 4' x 4' pegboard filled with measuring tools.
I have an illness. I know.