This game is not very intuitive. For those who are confused, this is what you do. First, click-and-hold anywhere in the upper-portion of the screen and this moves you through the clouds. You can go upper-left, center, or upper-right.
Go through the clouds until you come to some character. They may have a bubble over their head of some other character they want you to go to (but also you can just ignore this). The main thing is if they give you an item, which goes somewhere at the bottom.
So now go through and try to give items to the characters as you meet them. There's really no reason not to try every item you have with every character you meet.
If you give the right item to a character they will give you an item as well. Some items must be given to multiple characters, so you'll have to go through the sequence again re-getting items until you got that one, then give to some other character.
In addition to some items needing to be given to multiple characters, some characters need multiple items, some characters never need any item, and some items are never used (beyond collecting it)
If you already have the item a character would have given you in exchange for some item, no problem, because you won't lose your item in that case. (Useful because you may also need to give that item to someone else).
So basically fly through the clouds and do all of the above a bunch.
The star is the very first item and you are given this for free if you talk to the right character any time you don't have a star. So this will allow you to re-do any sequence and re-collect items you've used.
Don't use the airplane item until you've collected all the other items at least once because this item ends the game, so you may be missing some medals otherwise.