To sew a blanket stitch on polar fleece, start by trimming away the selvage edges of the fabric with a rotary cutter or scissors. Then fold over the cut edge by 1/4 inch to create a smooth edge around the fabric. Pin the cut edge of the fleece in place every few inches with straight pins.
Thread a needle with embroidery thread. Make a sewer's knot at the end of the thread, and stitch through the fold on the end of the polar fleece to hide the knot and thread tail. Push the needle through the wrong side of fabric 1/4 inch directly below where the thread emerged from the top of the fabric fold. Pull the stitch taut. The needle should now be on the right side of the fabric. Turn the fabric over, and begin working on the right side of the fabric.
Insert your needle through the front of the fabric approximately 1/4 inch from the edge of the fleece and 1/4 away from your first stitch. When you pull the thread through the fabric, leave a little loop on the front side. Thread your needle through the loop on the front side of the fabric. Pull the thread so it lies smoothly against the fleece, but do not pull so tight as to bunch the edge of the fleece.
Make a second stitch, starting from the front of the fabric, that is 1/4 inch away from the edge and 1/4 inch from the last stitch. Again, leave a small loop of thread when making this stitch, and then catch the loop with your needle to create the blanket stitch. Continue stitching until you completely finish the blanket's edge.