There are many ways to get this done and i will mention each of them one by one.
1.Download Helper-I have mentioned about this handy peace of addon many times in BW and i still think its a must have to all firefox users.It can rip off any streaming content on the internet as simple as a click.The addon is Download Helper.You need to have firefox to install it.
>>>>Install Download helper addon.
>>>>Go to last.fm.
>>>>Play the song of your choice.
>>>>The Download helper's sign of detecting streaming content '3 ballons' will start rotating just to the right of the address bar.
>>>>Click on it and you will find the streaming files.
>>>>Click again on the required file and your download will start.
You can download Download helper plugin from here.
2.Orbit Downloader-One of the best download-assistants released till date.Fast and flexible.Many features inbuilt.Read my detailed article on downloading streaming content using Orbit Downloader.
3.Audacity-Sounds familiar?And you thought it could record only your voice.It can be used to record any sound on your computer.And you can use this feature for recording songs from Last.fm too.Read this to learn how to do that.