When the computer screen shows that you are already in maintenance mode you should also already be logged on as root. Then you simply run the fsck command on the system partition. For example if the system partition is /dev/hda1 you would enter the following command.
If the fsck command says that it doesn't support the -y option then just retype the command without the -y option. More information about fsck can be found in the manual pages. You can read the fsck manual page by entering the man fsck command.
Once you have done this then your system should not require you to do this very often. If you find that you have to do this frequently then you may have a hardware problem or you may be doing something such as turning off the power without shutting down Linux properly. Either way if you see this requirement to run fsck manually on the system partition more than once a year then something else is wrong. Most people would never see this or they would see it if their disk drive was failing.
If your Linux system does not have apt-get then you will have to install it from the CD-ROM that you used to install Linux. You probably will have to boot the CD-ROM and find some sort of system repair option. First see if you have apt-get by using the find command.
find / -name apt-get
If the find command lists apt-get somewhere such as /usr/bin/apt-get then your problem is probably that the directory containing apt-get is not in your path. If the find command does not list apt-get anywhere then it is probably missing.