NOTE: Sewing sleeves to something is a Moderately Easy skilled task.
Making the pattern for sleeves is more difficult.

The easiest way to make a sleeve pattern is to cut apart an existing garment, and then trace each piece.

You'll want to have measurements for around your shoulder, and around your upper arm.

A basic, "set-in" sleeve is shaped like this.

Add an inch or so to each of your measurements (in addition to the seam allowance), unless you have very stretchy fabric and want tighter sleeves.

The top bell curve corresponds with the measurement of your shoulder-armpit.

The widest part should correspond with your upper arm measurement.

With this basic sleeve shape, you can make short sleeves, 3/4 sleeves, and long sleeves.

To determine how long you want your sleeve, measure from shoulder to where you want the cuff to hit and also armpit to cuff.

The tutorial for attaching sleeves is here: Easy Sleeves

For a flared sleeve, instead of tapering the sleeve down to the wrist, make the sleeve flare back out after the elbow. The wider the end of the sleeve, the more the sleeve will flare.

For a puff sleeve, you'll want to cut a wider sleeve that's similar in shape to the basic sleeve.
In this example, I've added 8 inches to the shoulder and upper arm measurements, which would yield a very big puff.
For a gentler puff, add 3-4 inches.

Gather or ruffle where shown, so that after ruffling the measurements matches your own.
I like to pin each end and the center to the armhole, and then gather the sleeve, pinning the gathers in place.