First, empty the Trash if you haven't already done so. Then reboot. That will temporarily free up some space.
According to Apple documentation, you need at least 9 GB of available space on the startup volume (as shown in the Finder Info window) for normal operation. You also need enough space left over to allow for growth of your data. As far as I know, there is no performance advantage to having more available space than the minimum Apple recommends. Available storage space that you'll never use is wasted space.
If you're using Time Machine to back up a portable Mac, some of the available space will be used to make local snapshots, which are backup copies of files you've recently deleted. The space occupied by local snapshots is reported as available by the Finder, and should be considered as such. In the Storage display of System Information, local snapshots are shown as "Backups." The snapshots are automatically deleted when they expire or when free space falls below a certain level. You ordinarily don't need to, and should not, delete local snapshots yourself.
To locate large files, you can use Spotlight as described here. That method may not find large folders that contain a lot of small files.
You can also use a tool such as OmniDiskSweeper (ODS) to explore your volume and find out what's taking up the space. You can 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.
Proceed further only if the problem hasn't been solved.
ODS 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 ODS in the Applications folder as usual.
Triple-click the line of text below to select it, then copy the selected text to the Clipboard (command-C):
sudo /Applications/OmniDiskSweeper.app/Contents/MacOS/OmniDiskSweeper
Launch the 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. Click Utilities, then Terminal in the icon grid.
Paste into the Terminal window (command-V). You'll be prompted for your login password, which won't be displayed when you type it. You may get a one-time warning not to screw up. If you see a message that your username "is not in the sudoers file," then you're not logged in as an administrator.
I don't recommend that you make a habit of doing this. Don't delete anything while running ODS 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 you're done with ODS, quit it and also quit Terminal.
