1. Always iron before you cut your fabric! I also recommend light steam and a starch product (I love Best Press). This helps pre-shrink your fabric and stabilize it at the same time - making sewing/piecing easier. I have also noticed when I do this, I rarely need to use starch again, even when I final press my blocks.
2. Ensure your 1/4" seam EVERY time before you sew. Now if you are one of the lucky ones who owes a 1/4" presser foot with a guide - no need - I am very sure you can purchase them for all machines now days and I highly recommend it. I still make sure the guide isn't bent out of place and check my 1/4" seam regularly.
3. Pin, pin, pin! Pin as often as you can. This ensure your block seams match up perfectly.
4. Squaring up your blocks as you finish them.
5. When adding your borders do the following steps:
a. Lay your quilt top flat.
b. Measure left to right on the top, middle and bottom of pieced top. bor
c. Average those 3 measurements. Use this measurement to pre-cut your top and bottom border pieces.
d. Sew on top & bottom border pieces, using pins - pin at each end FIRST, pin in the center, then space pins between other pins about every 3-4".
e. Press your borders.
f. Repeat step a - e again for the left and right borders.
I teach these things in my Beginner Quilting classes, I don't teach perfection, I teach accuracy and how to "fix" things if need be. I feel strongly if you follow these "key" steps, your top will end up square.