As you have no doubt discovered, there are many ways to hand appliqué. Traditionally, the shapes were cut with 1/8 extra seam allowance and the shape was pinned to the background fabric and you used the tip of your needle to turn under that seam allowance as you stitch. This is called needle turn appliqué.
Some people like to prepare their pieces by turning under the seam allowances on all their pieces using starch or freezer paper first before stitching. You will need to watch a few YouTube videos to find out what method you want to use.