In Fedora if you go to /var/log there are several files and directories where all your logs are kept. You can't really tell how has been scanning your ports because a port scan is a legitimate TCP request to establish a connection to a specified port. You may see a list of ports scanned by one individual host which may be indicative of a port scan. Depending on your menu layout, you should be able to go to System -> Administration -> System Log to view all of these logs in a graphical format.
If you want something a little more evident, you should look into installing an Intrusion Detection System (IDS). One well-known IDS is called Snort