The first consequence of a full home directory ("over quota") is the inability to login from the graphical desktop environment. You can always login from the command line (Alt-Control-F1 until F6) in order to delete unnecessary files - directories.

Useful commands are:

• quota (displays users' disk usage and limits)
• du -sh ~ (displays the file system block usage for the home directory)

The du command can show the size of files/directories: 
 

• du -sh ~/* | sort -hr | more (for files/directories with names beginning with a letter or number)
• du -sh ~/.??* | sort -hr | more (for files/directories with names beginning with a dot)

After this procedure, delete or remove outside your account the bigger files/directories.