An assembled sleeve isn't much more than a tube of fabric, but completely disassembled, it looks more complicated.
If you are inexperienced with tailoring, this "quick and dirty" tutorial looks like a good start: How to tailor a sleeve. It requires you to put on the shirt (or dress) inside out, gather the surplus fabric at the existing seams and pin it to your desired size. You then open the original seams, sew along the pin lines and trim and neaten your new seams.
What it doesn't explain is how you match the new sleeve seam to the existing side seam of the bodice.
If you want to reduce the size of the bodice as well, it's perfect to do both at the same time. Otherwise you either need to match the new sleeve seam up to the original side seam (which preserves the puffiness at the shoulders) or you need to sew the sleeve seam in a crooked line back down to the side seam (which artificially narrows the arm hole).
I suggest going with the first solution, because it's the neatest and an armhole that's too narrow is very uncomfortable. This solution is shown in this video: Resize oversized sleeves
The professional way is to dissassemble the sleeves, adjusting the cut of the pieces and reattatching them to the dress. Of course this is more complicated, but if the "quick and dirty" solution doesn't look good, this is the only way to make it look perfect.
First of all, mark which sleeve is the left one and which is the right one, because they may differ very slightly from each other and sewing the left sleeve to the right armhole looks strange and feels uncomfortable.
Then take your measurements as described in Create custom sleeve pattern. Keep in mind that you want to measure your desired sleeve, so if you don't want it to be skin tight, don' t measure skin tight.
Follow that same instruction and construct your new sleeve on a big sheet of paper. Once you're done, measure the circumference of the armhole in your bodice. Then measure the length of the "sleeve crown", the curved line on top, from seam to seam. The sleeve crown should be slightly longer than the circumference of the arm hole.
If your sleeves have cuffs like shown in the picture, reattach them after closing the long sleeve seam.
At the end, sew the sleeves back onto the bodice as shown here: How to insert sleeves.