Float Sidequest in Surgate Castle
Float can first be acquired when you visit Surgate Castle which is found on World 2. In the castle's library you'll find a man standing in the southeast corner who complains to you that no one puts the books back in the proper places. Along the desks in the southern most portion of this room you'll find three books which you need to put on the bookshelves throughout the room. If you mess this puzzle up, leave the room to reset it.
The three books that you need to put back on the shelves are...
Register of Monsters
When you approach each bookshelf and inspect it, you'll be told what letters go there. You'd assume that the shelves start with A and 1 by 1 escalate throughout the alphabet but this isn't how it works. To make things easier for everyone, I have marked which bookshelves correspond to which letters below. Click on the picture to enlarge it.
After putting all the books in their correct places, speak with the NPC again and he'll open up a secret passage in the northeastern most portion of the room. This passage takes you to a few different areas, the first of which has a chest with 5000 GP inside.
When you find yourself outside travel under the bridge and to the western tower of the castle. Go up the stairs until you find yourself in the same room that's shown in my screen shot below - which is where you'll find Float.