How do I set in a sleeve without puckers?

A set-in sleeve has more fabric in the cap than in the armhole it goes into. That extra is meant to be eased, not gathered.

Run two rows of long stitches in the cap between the notches, just inside and just outside the seam line. Pull the bobbin threads gently to draw the cap in — enough to make it fit, no more. You want a smooth curve, not visible folds.

Match the notches. Sleeve caps are asymmetric: the front notch is single, the back double. Getting them the wrong way round puts the sleeve in backwards, and it will pull across the shoulder in wear.

Pin from the sleeve side, with the sleeve uppermost, at the notches and the shoulder point first, then distribute the ease between them. Most of the ease belongs across the top of the cap, not near the underarm.

Sew with the sleeve side up so you can see and manage the ease as it feeds.

Press the cap over a ham, not flat. A sleeve cap is a three-dimensional shape and pressing it flat creases the ease you just worked in.

If it puckers, unpick that section and redistribute rather than trying to press it out. Puckers in a sleeve cap do not press out.