I recently exprience one problem that requires a patch. I downloaded that file .patch, but have no idea how properly to install that to my hosted website.
If you can shell into the account, you
cd /var/www/somewhere/docroot/sites/all/module patch -p1 < /path/to/the/patchfile
Depending on how the patch was rolled, you may need to adjust the number after the -p to get it to apply properly. The man page can give you more details.
If you can't shell into the host, then you need to downloads the files(s), apply the patch locally and then upload them. This question give guidance, or you can cut to the chase and check out TortoiseMerge.