in windoz or Mac OSX os, get HashTab
and install it.
Right click on the *.iso, select Properties and then "File Hashes" Tab. It auotmatically calculates MD5, CRC32 and SHA-1
in linux, in a shell
calculates the md5 hash and displays it.
Then compare the result to the <iso_name>.md5 file content. (or in windoz compare to the SHA-1 value)
c97d567e913b1d81314108757d85efcb is the md5 number to use for comparison.
In Linux, K3B automatically calculates the MD5 hash so you can burn and check at the same time.
Note that a download using a bittorrent client also checks the integrity of the downloaded files so no need to check it again unless you just want to.
Finally, if you are burning the iso to CD|DVD, what really needs to be checked is that the burn was properly done. K3B and most burner SW have an option to check the disk. Use it.
TIP: It is not necessary to check every character of that long hash sequence. As long as the last 4 are matched & in the same location of the sequence, both strings are the same.