Grooveshark lets you and your pupils queue up songs and record spoken word interludes between each song.
Spoken interludes are recorded using Grooveshark's built
in recorder. Voice interludes cannot 'overlap' with the music.
Fancier jingles can be inserted, but these need to be pre-uploaded into your Grooveshark account as songs in their own right first and then added to your playlist.
Shows can listened to again, but without the spoken interludes (these can only be heard as the broadcast goes out 'live').
If you want to broadcast live and have voice overs which overlap with the music then you need to combine Grooveshark with another free service, Mixlr.
Alternatively, you can broadcast live using an iOS device using the free Mixlr app. This will broadcast anything that is picked up by the device microphone, allowing pupils to play music using Grooveshark (or anything else for that matter) on a device that the mic can pick up and then talk over it.
Podcasting is a slightly different process in that the podcast need to be recorded and edited before being shared online. Also as a rule of thumb it cannot contain commercial music (unlike the two options above) but it can contain Creative Commons licensed music.