I'd like to know how to verify downloaded files against checksums such as md5, sha1 and crc32.

I found a few files that come with md5 and sha1 files, however I don't know how it works. I have the valid md5 and sha1 checksum in the file but I need to retrieve the file's checksum to verify it against the md5 and sha1 files.

How do I do that?

Ok so there are many downloads on this site and each has an MD5 hash. How do I check if my downloaded file is not corrupted with that MD5 hash?

You normally need to get the checksum checker from the site you downloaded from. As far as I am aware there is not generic way to check.

So look on download site for a program to run which produces checksum and them compare with declared checksum.

To be honest it is a long time since I remember getting a corrupt file, so I would not worry about it. The downloading includes checking each block of data that is down loaded. If it does not arrive correctly then it is resent automatically.