It really does just take time. When I first started quilting I had lots of problems with things lining up. After 20 years I'm better at it. :)
Absolutely critical to cut accurate and even more important to sew a CONSISTENT seam allowance. If you don't have a machine that can move the needle to the 1/4" setting then get a 1/4" foot. The best thing I ever did to help with accuracy was getting my Viking 830 that has the needle setting. The 1.8 setting is 1/4" and I move it one tick more to 2.0. I just did a quilt with 48 blocks that have 1 1/2" pieces and I didn't need to square up anything, they all came out great.