For information about the Other category in the Storage display, see this support article. If the display seems to be inaccurate, try rebuilding the Spotlight index.
Empty the Trash if you haven't already done so. If you use iPhoto, empty its internal Trash first:
iPhoto ▹ Empty Trash
Do the same in other applications, such as Aperture, that have an internal Trash feature. Then restart the computer. That will temporarily free up some space.
See this support article for some simple ways to free up storage space.
You can more effectively use a tool such as OmniDiskSweeper (ODS) or GrandPerspective (GP) to explore the volume and find out what's taking up the space. You can also delete files with it, but don't do that unless you're sure that you know what you're deleting and that all data is safely backed up. That means you have multiple backups, not just one. Note that ODS only works with OS X 10.8 or later. If you're running an older OS version, use GP.
Deleting files inside a photo or iTunes library will corrupt the library. Changes to such a library must be made from within the application that created it. The same goes for Mail files.
Proceed further only if the problem isn't solved by the above steps.
ODS or GP can't see the whole filesystem when you run it just by double-clicking; it only sees files that you have permission to read. To see everything, you have to run it as root.
Back up all data now.
Install the app in the Applications folder as usual. Quit it if it's running.
Triple-click anywhere in the corresponding line of text below on this page to select it, then copy the selected text to the Clipboard by pressing the key combination command-C.
For ODS:
security execute-with-privileges /A*/OmniDiskSweeper.app/*/M*/* 2>&-
For GP:
security execute-with-privileges /A*/GrandPerspective.app/*/M*/* 2>&-
Launch the built-in Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
Paste into the Terminal window by pressing command-V. You'll be prompted for your login password.
The application window will open behind other open windows. When you scan a volume, the window will eventually show all files in all folders, sorted by size. It may take a few minutes for the app to finish scanning.
I don't recommend that you make a habit of doing this. Don't delete anything as root. If something needs to be deleted, make sure you know what it is and how it got there, and then delete it by other, safer, means. When in doubt, leave it alone or ask for guidance.
When you're done with the app, quit it and also quit Terminal.
