The band has been releasing a number of short videos in conjunction with the new CD; below you can see live rehearsal footage for "Battle in Me." You can see this and the other videos on the Garbage YouTube page.
At the Spin preview page for "Not Your Kind of People" you can also find an interview the magazine did with Garbage singer Shirley Manson, and her recollections of recording each of the band's albums.
Update: Garbage announced on Twitter today that you can get a free download of its song "Automatic Systematic Habit" at iTunes this week (U.S. only).
Garbage began its tour on May 5th in Los Angeles and continues throughout the spring and summer, playing headlining gigs (many of them already sold out) and festivals in the U.S. and abroad. (Find all Garbage tour dates here.)