Pulling a thread to tighten the connection between the parts of clothing:[1]

A clothing which was sturdily sewed and its thread was left sticking out[2], and two parts of the clothing slightly split apart from each other with the threads of the sewing sticking out, then if one pulls the head of the threads in order to tighten and connect the two sides, it is considered sewing and one is liable [to bring a sin offering]. [This applies] even if one has not made a knot [at its end] if [the amount that the clothing have reconnected] is like the amount of three stitches.

Pulling the thread that tightens the sleeves of shirts: Those [people] who tighten their clothing around their arms through [pulling] a thread which pulls and tightens it, [are forbidden to do so as it] is forbidden to pull [such a thread] on Shabbos due to the sewing prohibition.

The reason it is forbidden: (Now, although the sewing is not one that will last being that one only tightens it at the time that he wears it while at the time that he removes it he loosens it, nevertheless it is Rabbinically forbidden being that it is similar to sewing.)

If the holes are wide, round, and sewed: It is only allowed if [the shirt] has slightly wide holes which are fixed in with sewing and [the hole is] round in circumference, in which case it is no longer similar to sewing[3].

Walking into a public domain with a needle attached to this thread: [In the above circumstance that the holes are wide, round and fixed with sewing] then even if the thread is inserted into a sewing needle [a needle with a hole] it is permitted to go out with it [into a public domain] since it is always connected to the thread, and the thread [is always connected] to the clothing, and it is thus an accessory to the clothing.    

If one is able to remove the clothing without loosening the tightened thread: If the clothing is not greatly tightened by this thread to the point that one must loosen it when he removes [the clothing in order so it come off], but rather at times he changes his mind and decides to leave it this way eternally being that he is [anyways] able to remove it this way with it remaining slightly tightened, then it is forbidden to tighten it on Shabbos in all cases [even if the holes are wide and round and are fixed with sewing, and even if he does plan to loosen it].

The reason for this is: because perhaps one will change his mind and decide to leave it this way for ever, and it is thus found that he made a sewing which will last, and by a permanent sewing it does not help the fact that the holes are wide and are fixed with sewing and are round.  

Summary:

It is forbidden to tighten two loose parts of a cloth by pulling at the thread that is sticking out, even if one is doing so for temporary use, like to undo that day.[4] Thus the sleeves of a shirt which have a thread which is pulled on in order to tighten may not be used unless a) the hole from where the thread protrudes is round and b) the hole is fixed in by having been stitched around its circumference, and c) One is unable to remove the sleeve without loosening the thread, thus guaranteeing that one will not leave it permanently in its tightened state.

Q&A

May one pull the drawstring[5] of a garbage bag or sweat pants to tighten it?

Yes. This may be done even if one plans to leave it tightened permanently, as the above is not similar at all to sewing being that its holes [which contain the draw strings] are large and the string itself is not at all similar to a thread. 

May one tighten a loose button through pulling on one of its threads?[6]

Doing so is forbidden due to the sewing prohibition.