Putting in a set-in sleeve (version 1)

My first fitted sleeve.

Fitted (set-in) sleeves aren't hard, but they can be a little fussy, and they definitely require patience and a careful hand when sewing in. And it's a great feeling when you turn the sleeve out and see a clean join without puckers or wrinkles.

Equipment
I highly recommend getting a tailor's ham before you start putting in fitted sleeves -- It's not too much money and it makes the part where you iron the seam flat much, much easier. For most sleeves a proper sleeve roll or sleeve board isn't necessary, but I have to admit I do like mine a lot. If you can only get one, definitely get the ham first and get the sleeve roll/board later because the ham will come in handy for many different sewing projects.

Cutting out
When you're cutting out a fitted sleeve, there will be a bell shape where the sleeve will join with the shoulder of the shirt. There will be notches on either side of this curve (and usually a few dots in between) -- one side will have a single notch and one side will have a double notch--these will correspond to single and double notches on the front and back armholes. When you're cutting out the pattern, you definitely want to pay attention to the cutting layout's instructions. If you're not able to fit the sleeve piece on a folded piece of fabric during the cutting layout and you have to cut the sleeve piece out twice, mind your p's and q's about the right/wrong side of both the fabric and the pattern piece, because those notches will tell you which side is the front and the back of the sleeve when you're trying to put it in, and it would be very easy to end up with "two left sleeves" so to speak if you have the notches in the same orientation for both sleeves.

So far I've run into two ways to put in a fitted sleeve. Version 1 appears to be the more common way. If you did the previous tunic project, you've done this already.  This involves stitching the front and back of the shirt together at the side-seams and shoulders, easestitching along the sleeve's shoulder, then stitching and hemming the sleeve arm, then fitting the sleeve into the armhole of the shirt with a slight gather and joining from there.