well, there are 4 different types of sleeves, really:
raglan: triangular sleeves that run up to the neck line. You see that on "College shirts" a lot. just google raglan.
For that you have to decrease your backpiece from the place the sleeves beginn at. Cast off about 3 stitches on each side and then decrease evenly until the top to form a nice line (take pics and patterns of ralgan pieces as example).
then you knit the sleeve (straight or getting wider) until the joining point, cast off the same amount of stitches and do the same decrease to make pieces join smoothly.
you can also do sleeves with a round sleeve cap. Then the shaping is way more of an issue and I am no master in making it.
Or you do an "inset sleeve": the sleeve is "rectangular" in the way it is set in (and not shaped round). Fits pretty well on kids, really.
The last option I see, I would decrease for the arm holes and then sew the piece up. Pick up stitches around the arm holes and knit the sleeves down (then they deffinitely fit at the top). Maybe consider short rows for shaping here. There is a video for it, too.