One way to make a sweatshirt is to buy the appropriate material and follow a pattern. Alternatively, it's possible to take an old sweatshirt and update it into a new design.
Companies such as McCalls and Linden produce patterns for making sweatshirts at home. Fabric stores sell sweatshirt fleece, though the patterns are appropriate for sweater knits, jersey and knitted velour. The required amount of fabric depends on the size and design, but roughly 2 yards is common. It's also necessary to buy ribbing and matching thread.
Following a pattern requires cutting out the pattern pieces and pinning them to the fabric as instructed. It's necessary to follow the fabric grain so the finished garment falls correctly. Next, pin the pieces as instructed, and sew using the suggested seam allowances. Finish with ribbing at the neck and cuffs.
Dressing up an old sweatshirt is another option for producing a new garment. One method is to cut out a patchwork design from pillowcase or quilt. Fuse this to the front of the sweatshirt, and stitch around the design.
To make a peek-a-boo lace insert, cut a circle out of the back of the sweatshirt. Trace the cutout onto lace, and cut the circle 1/2-inch wider all around. Pin the lace to the hole, and sew all the way around. This technique is suitable for both a standard sweatshirt and a hoodie style.