A top option is using Thangles, in the proper size for the block you are planning. If you don't have these, try the method I show below. It may be familiar to you, but maybe not.
Step 1: Cut squares of light and dark fabrics the proper size. What is the proper size? The size of your finished square plus 7/8 inches. For my project, each square finishes at 1 inch, so I cut my squares 1 and 7/8 inches on a side. For a finished measurement of 1.5 inches, cut your squares 2 and 3/8 inches in size.
Step 2: Draw a diagonal line on your light colored square of fabric. Take a dark fabric, right side up, and place a light square, right side down, on top of it, all corners aligned. See the photo below.
Step 3: Sew 1/4 inch to the left of the diagonal line on your light fabric. Use your 1/4 inch presser foot if you have one. See photo above. You can chain piece a number of these.
Step 4: Take the squares out, turn them around, and sew down 1/4 inch away from the diagonal line, on the other side. See the photo above - sorry can't see my thread too well!
Step 5: Cut along the diagonal line with a rotary cutter and a ruler. Here I took the photo of the back.
Step 6: Press open, carefully. It's easy to stretch these along the bias of the fabric. Measure. If your target finished size is 1 inch, the unfinished size of these units should be 1.5 inches squares. Check to see.