LastFM is a "scrobbler" client for the Last.FM service. The application keeps a record of what music you listen to on your Mac, and then sends that data to the Last.FM servers. This way, the service gets the information of what kind of music you like, so it can automatically recommend similar music for you when you listen to Last.FM radio. The application also allows you to listen to Last.FM radio stations, but I couldn't get this feature to work.
When you first install the app, you will be asked to let LastFM access your iTunes listening history. This is a great way of letting the app know what you like. After that, you will be taken to the main window. You will notice that there are some controls on the top. These are My Profile, Share, Tag, Playlist, Love, Ban, Play, Skip and a volume control bar. You can access recently played songs and other features on a toolbar on the left part of the window.
If you want to start listening to a radio station, all you have to do is type in the name of the artist, and Last.FM will find a station for you and start playing it. I did this without problems, but even though the station started playing, I didn't get any sound. I tried different stations and re-starting the app, but to no avail.