Summarize:

If your body piece is already intact and your sleeves are sewn up along the bottom edges as well, then you can attach the sleeves by matching up the seams of your sleeves and armhole openings. Turn the body piece inside out and leave the sleeves right-side out. Slip one of the sleeves through one of the armhole openings wrist first. Keep sliding the sleeve into the opening until the edges of the armhole opening and the shoulder area of the sleeve are aligned. Identify the seam on the bottom edge of your sleeve and on the bottom edge of the armhole opening. Place a pin to secure the seams together. Then, pin around the rest of the sleeve and armhole opening to connect them. Make sure to distribute the fabric evenly and pin the fabric together so that the raw edges are facing each other.  You may also pin the center point of the shoulder to the shoulder seam on the armhole opening for increased accuracy. Make sure that the correct sides of the fabric are facing each other and the raw edges are lined up. When you have finished pinning your sleeve into place, use your sewing machine to sew a straight stitch around the edges of the sleeve and armhole opening to secure the pieces together. Sew about 0.5 inches (1.3 cm) from the raw edges of the fabric.  Remove the pins as you sew. Cut the excess threads when you are finished sewing. After you finish attaching 1 sleeve using this process, you will still need to attach the other sleeve. Repeat the steps to attach the other sleeve to your body piece.
Turn the body piece inside-out and slip the right-side-out sleeve in wrist-first. Pin the sleeve to your armhole opening. Sew along the edges. Repeat the process for the other sleeve.