Set-in sleeves are tricky, and there is an easier method.

This method is still good to know, because you might find yourself in a situation where you want to modify/add sleeves to a top that already has the side seams sewn up, or doesn't have side seams.

So here we go. We're starting with the side and shoulders seams already sewn, so we have a basic sleeveless top. The sleeves have also been sewn up and cuffed.

You can ignore the hood in the bottom right hand corner. That's for later.

This is each sleeve folded in half.

Mark the folded edge at the longest point with a pin(red dots), and the shortest edge (green dots).

The green dots will wind up in the armpit area and the red dots at the shoulder.

Turn the top inside out.

Keep the sleeves right side out, and insert them cuff-end first into the arm holes.

Match up the armpits and the shoulders.

Here's a sleeve inside the shirt with the edges lined up with the armhole.

Pin around the armhole- you may have to "ease" the sleeve into the armhole a bit, which means stretching it to fit.