Thanks, everyone!
Susy, I agree with quiltncrazy that measuring is important. My sampler blocks are all going to be 12" squares. I got a 12" square book of graph paper at JoAnn Fabrics and drew it out at actual size. Then I measured each piece and added the seam allowances. For example, my finished pieces (except for the center square) were all 1 1/4" thick. Adding in a 1/4" seam allowance on each side means adding 1/2" total. So I cut each piece 1 3/4" wide. Added the same 1/2" to the lengths.
I used a rotary cutter but even then am not always precise. So when I marked my sewing lines, I made sure they were the finished piece size apart, even if the seam allowances were off a tad. And if one of my stitches went off the marked line, I pulled it back out and redid it.
Ironing plays a part, too. Each piece must be ironed flat so nothing hangs over the seam or you lose width.
The big thing for me was realizing that you add each piece by going around and around. You add the smallest top piece to the center square, then the smallest right-side piece, then the smallest bottom piece, left-side, then the next top one and so on.