hard. Really, don't be too discouraged. It took me many tries at sewing in sleeves before I was confident that I could do it.
I think its really important to not be intimidated to try things that aren't always easy. Even if you make a complete botch of things it pushes you to learn new techniques and thats what will make you a better seamstress.
There could be a number of things going on here, its very difficult to see whats happening from your pictures. As already mentioned, your sleeve pattern could be wrong and thats why your having such a hard time. A sleeve should not be just a long rectangle shape. It will never work if you cut it out like that. If thats whats wrong this wont help and you will need to re-cut the pattern pieces.
What I think has happened is you have caught the sleeve fabric in the machine when you have sewn it on and or your seam allowance was not an even 3/8" all the way around. It could be this and a combination of the wrong pattern cut out, hopefully its just the first reasons and it can be fixed.
First off, carefully unpick your sleeve and and as much of the armhole seam as you can.
1.Ease stitch within the seam allowance along the curved edge of the sleeve pattern piece as shown above. Stop and start sewing before the curve of the edge of the pattern piece shape changes direction.
This means two rows of stitching 1/8 " or 3mm parallel to each other. You can later pull the bobbin thread to "ease" the shape of the sleeve so don't use an ultra small machine stitch.
2. Pin and sew up the armhole seam.
Sew from the point you unpicked it, in the direction of the blue arrow (A) Otherwise you might end up with (B)
Press the seam open with an iron
3. Insert the sleeve inside the garment so the fabric is right sides together as in (A) Pin the sleeve all the way round and ease up the fullness to get a good, even fit. (Pull the bobbin thread to ease) Tack/ baste the sleeve in by hand. This is important to check the fit and evenness of your ease, you don't want ruffles.
4. Take out the tacking and press the sleeve along the seamline taking out all the puckers. A is an iron B is the ironing board and C is the sleeve. hehehe
5. Baste the sleeve back into place, fabric right sides together and underarm seams in line with each other as before.
The blue is the garment, the black is the sleeve. The big gray needle with the orange thread in pic A is how the machine needle should go in. I hope it kind of makes sense.
This bit is the trick/ skill to sleeves. Very carefully machine stitch an even 3/8" along the seamline. Sew all the way round. Use your free hand to smooth the fabric so it goes under the needle flat. ***Make sure you don't just have a smooth top fabric and the bottom fabric puckered and lumpy.***
You can stitch two parallel rows of stitching to be sure its not going to fall apart.
B. Cut off/ clip your excess seam allowance.
Finished Hoorah! Turn right side out and pimp around craftster. . Be sure to post the pics Vylent!
Just to quickly add. If it is that you've cut the wrong pattern shapes you might be able to still fix it rather than just starting again. You could recut the armhole and recut the top of the sleeve to the right shape. You could then just add a wider cuff on the bottom. Whatever you decide don't give up.
The pic ideas I stole from "Complete guide to sewing" Get a copy if you can, its a real must have book. Most people do a variation on the above and when you've done a few sleeves you'll find ways to cut the time down in putting them in.
Not wanting to hijack your thread but maybe we should edit the original post title to put something like **TUTORIAL ADDED- Sewing in sleeves** so anyone else who's stuck can find the pics.