Use a secure terminal program to log onto the command line (often SSH Secure Shell terminal on computers using Windows or Terminal on computers using OS X).
At that point, type the command "quota -v":
This should tell you what space you have available.
Filesystem blocks quota limit grace files quota limit grace
/dev/home_volume 332 400000 420000 41 0 0
/dev/mail_volume 8 200000 220000 1 0 0
In this example, /dev/home_volume refers to your account's file space.
/dev/mail_volume refers to your inbox space.
On our system, a block is one kilobyte, so blocks shows you how many kilobytes you've used. Somewhat confusingly, there are actually two numbers that define how much space you can use. quota defines a "soft" limit that, should you need to, can be exceeded temporarily. limit, on the other hand, reflects the number you absolutely cannot go past.
If your usage is over the quota number, but under the limit, there will be an entry under the grace column telling you how long you can remain over quota before the system will prevent you from using any more space. If your usage is at or slightly below the limit, or if your grace period says none, you should remove files from the appropriate volume as soon as possible. Not doing say can result in odd and unfortunate behavior when you or the system attempt to modify existing files.