I've never used Spotify - However, for any App you wish to install on your Ipad, you tap the Apple App Store Icon and do a search for Spotify, or whatever app you are interested in. Some apps are free and some you need to pay for via an Apple Itunes Account. There is a Free Spotify App. You tap on install and the ipad will download the app after you tap in the Itunes Account Name and Password.
It would appear that you also need to have a spotify subscription to use it though!
Hope this helps
OOT.