Canonical had been testing Ubuntu One Music Store in a closed beta fashion for quite sometime. But starting yesterday, it has entered public beta. It means that everyone can start using this service, which is available as a plugin for Rhythmbox, the default music player in Ubuntu Linux.
To access this feature you need to have a UbuntuOne account, which comes with 2 GB of free space initially. After you buy music from UbuntuOne music store, they are transferred to your UbuntuOne account which can then be synchronized across all the computers using the same UbuntuOne account. The handy feature is that you can also use the UbuntuOne web feature to download these songs, for full offline access.
If you cannot find UbuntuOne music store in the Rhythmbox on your computer, search for the UbuntuOne music store plugin in the Ubuntu software center (Ubuntu 10.04 Lucid Lynx). You can then enable it going to Edit-> Plugins in Rhythmbox.