I start with the tee
I cut the tee up the sides, and out through the sleeve hems. Then I cut off the sleeves. I find it doesn't really matter where you cut the sleeves off, inside or outside the seam.
so I now have four pieces: front, back, and sleeves.
the sleeves are put wrong sides together, and the front and back are folded down the center. The pattern is placed on these three pieces, keeping in mind the placement of any graphics. Some times if the neckline is going to cut off too much or an important part of the graphic, I put it on the back.
next, I sew the shoulder seams which you can either serge or use a very narrow zig zag
then I serge the neckedge to give it some stability, and fold it over 1/4"
I then sew the neckedge down 1/4". You can also bind the neckline if you had extra fabric after cutting. I didn't have any extra with this tee shirt. Below is the finished new neckline.
Next is to add the sleeves. I just pin the center of the sleeve cap to the shoulder seam and serge it on adjusting as I go.
Now the tee is all sewn, except for side seams. It looks better already.
Last step (since my hems are already done) is to sew up the side seams. When using a serger, after I sew up the sides, I add a drop of fray check at the beginning and end of the seam since the hem is already done and is what will usually anchor the seam.
I now have a new tee, for the price of a cheap tee and less than an hour of my time.