A Spotify Premium account is currently $9.99 per month. Premium members do not have to listen to ads, can play any song, any time on any device, and can download music to listen offline.
A free account is supported by advertisements, and does not allow offline listening or the ability to choose songs on demand.
You can download the app for free from the App Store. It is compatible with the iPad, iPhone and iPod touch, and requires iOS 6 or later to work.