When knitting a sleeve, there are dozens of variations, but only a few basic categories.
These patterns start at the top and work their way down the body of the sweater. When you get to the armhole portion, where the sleeves separate from the sweater, you place the sleeve stitches on stitch holders and continue working around the body of your sweater. Then you'll come back after the body is done and work each sleeve separately.
Raglan sleeves are commonly made in this fashion. These sleeves have shoulder caps that aren't specifically fitted for the wearer, but they can't be beat for ease of construction.
From here, you can either work your sleeves in the round, so there is no need to seam the sleeve later. Or, you can knit your sleeve flat and sew it closed later. I've done both methods and have to say, for a shorter sleeve, seaming it later is fine. But for a full sleeve, I'm a fan of cutting down the work and making it in the round. This Little Girl Cardigan pattern is a great example of a raglan sleeve.
This type of sweater is knitted all in flat-knit pieces and then sewn together after all the pieces are finished. This is a drop sleeve with straight seams.
As in this purple baby's sweater, the sleeve is knitted as a flat piece. It will be sewn on to the back and front of the sweater, and then the seam will be sewn shut.
The best fit to a sleeve will always be in a set-in sleeve that can be customized to the measurements of its intended wearer. A set-in sleeve can be worked top-down or in pieces, but differs from raglan and drop sleeves in the amount of shaping it takes to make the sleeve cap fit perfectly. The Seamless Artemisia Sweater Craftsy class can help you perfect the process of making set-in sleeves.
This project is a yoke knitted sleeve.
Here, I've started in the round at one cuff and have worked that entire sleeve before getting to the yoke, where I've stopped working in the round. I knitted across the front of the sweater to where the second sleeve should pick up.
Then, I went back and knitted across the back of the sweater to that same spot.
Finally, I rejoined all of my work and will soon go back to knitting in the round as I work down to the second cuff. (The body of the sweater will be picked up after the yoke and sleeves are fully done, and will then be knit in the round to the bottom hem of the sweater.)
Dolman sleeves are another way of working cuff to cuff, but with the variations that you work the entire body of the sweater at the same time, usually as a flat piece. You start at one cuff, knit the body, then finish on the second sleeve. Coming off your needle, you'll have a piece that looks roughly like a cross with a hole in the middle. To finish the project, you will fold the flat knit piece in half and sew up the side and arm seams. A Dolman piece can also be worked hem to hem.
Or, as in this Dolman striped top, it can be knit in two pieces: front and back.
Ready to try your hand at knitted sleeves? The Perfect Fit Seamless Lace Cardigan is the perfect first sweater to knit.