The Shulhan Aruch (Orah Haim 340:7) addresses the case of shirts that have lacing on the sleeves, and people would pull the string to tighten the cuffs around the arm. Pulling the string is permissible on Shabbat, the Shulhan Aruch writes, and is not considered tying.
On the basis of this ruling, Hacham Ovadia Yosef writes that it is permissible to pull the string of a hood on a raincoat, for example, to tighten it. Moreover, Hacham Ovadia ruled that one is allowed to attach a hood to a coat with snaps or a zipper, and to attach the lining of a coat, if it is needed on Shabbat.
Attaching two items together with glue is forbidden on Shabbat. Thus, for example, one may not attach a "Post it" sticker to a surface on Shabbat.
The Shulhan Aruch writes that it is forbidden on Shabbat to make a pillow by filling material with feathers, as this falls under the prohibition of Metaken Mana ("repairing a utensil"). However, Hacham Ovadia writes that it is permissible on Shabbat to inflate a ball for a child or an inflatable mattress that is needed for Shabbat, even with a handpump. He adds that it is also permissible to blow up a balloon on Shabbat, though one may not tie the balloon. These rulings appear in Hazon Ovadia – Shabbat (p. 370).
The Shabbat prohibition of Me’amer forbids collecting produce that grew from the ground from the area where they grew. Therefore, Hacham Bension Abba Shaul (1924-1998) writes that if one has a fruit tree in his backyard, and the fruits fell to the ground, then although he is allowed to pick up individual fruits to eat, he may not collect them into a bag or basket, and doing so violates the Torah prohibition of Me’amer. If the fruits are not still under the tree, but are still outside, then the Torah prohibition of Me’amer does not apply, but it is nevertheless forbidden to collect the fruit, because this constitutes "Ubdin De’hol" (performing weekday activities on Shabbat). Once the fruit is in the house, however, it is considered "collected," and thus if the fruits are scattered on the floor, it is entirely permissible to collect them.
Summary: It is permissible to tighten the hood of one’s coat with a string on Shabbat, or to attach the hood or lining with snaps or a zipper. It is forbidden to attach items with glue on Shabbat. It is forbidden to fill a pillow with feathers on Shabbat, but one may inflate a ball or inflatable mattress. It is permissible to inflate a balloon on Shabbat, but one may not tie it. It is forbidden on Shabbat to collect fruit that is scattered outdoors, but in the home, this is allowed.