Just wondering if someone could suggest a PHP library that would allow me to read the data of an RSS feed and write it to a MySQL database. Also, if possible, provide a link
Reading data that simple is something you could use simplexml for.
http://www.ibm.com/developerworks/library/x-simplexml.html
From there you can see how easy it is to grab the data, instead of displaying, you store in a database.
Gotchas: badly formatted rss (see above tut) different flavours of rss (ditto) evil values in the rss - it's foreign data and should be handled with suspicion dependency on allow_url_fopen - maybe use cURL