Ok, so lets say you download 64-bit Linux Mint. You then download the checksums file:
http://ftp.is.co.za/mirror/linuxmint.../sha256sum.txt
Many distros have separate checksum files that are specific to the iso that you download, while Mint has all the checksums in one file.
So after you download the linuxmint-16-kde-dvd-64bit.iso and the sha256sum.txt into the same directory, then you can open a terminal at that location, and run 'rhash -c sha256sum.txt' and that will check all the checksums listed in the file against the iso if it exists. You can also do the same using 'sha256sum -c sha256sum.txt', and most checksum programs use the '-c' option to check checksums.
Another way you could do it is just run 'rhash linuxmint-16-kde-dvd-64bit.iso' and check the checksum yourself, visually with the listed one.
If this is not the answer you wanted, then please provide a concrete example of what is needed.