The two programs df and du can be used to monitor disk usage. Both programs will take a number of options. Your system may have information on these programs either in the man pages or in the info system.
The df program will report on disk space available for the filesystem which contains the directory you give it as an optional argument, or without a directory argument, for all filesystems in the mount table.
The du program will report on filesize totals for the directory given as an argument, and all subdirectories. If no directory argument is given, it defaults to the current directory.