If you have a large music collection in iTunes, iTunes Match is awesome! You get high quality copies of all songs it can match from the iTunes Store, your entire collection is avaliable, all the time, from any device, and iTunes Radio is ad-free. The annual cost is $24.99, or less than $0.10/day. This tip will focus on the "match" feature and ability to access your entire library from any internet connection.
You already have access to all iTunes music you've ever purchased, but what about those songs that you aquired from "other" places? Have any ripped CDs, MP3s from old-school Napster, or imported a hard drive with a friend's shared collection? iTunes Match wants to help.
For every song that you didn't download from the iTunes Music Store, iTunes Match will attempt to find a matched copy from the iTunes Music Store. If you have the old Matchbox 20 song "Push" as an MP3, you'll get access to a brand new high quality copy. What about songs that iTunes Match can't match? It will upload up to 25,000 songs to the iTunes servers from your library, and you'll still have access via the iTunes Match service, including from your iOS device. For more info on how to complete this process in iTunes, see the iTunes Match site at Apple.
Once your collection is fully analyzed, matched, and uploaded, you will want to toggle iTunes Match on for each of your iOS devices by going to Settings -> iTunes & App Store. Here you can also select whether to "Show All" music. This will show you all music in your library inside the Music app, even if it's not on your device. At the very bottom you can enable access to Cellular Data to download music.
Inside the Music app, with "Show All" enabled for Music, you'll see your entire collection. Songs that are not stored locally, but still in your library will have the cloud/down arrow icon to the right. Tap this icon to download, or just tap on the song to start it playing immediately.
In the screenshot tracks 1-4 are on the device, denoted by the absence of the cloud/down arrow icon. Track 5 is in the process of being downloaded, and the progress is tracked by the compleiution of the thick inside line of the circle. Tracks 6-8 are avaliable for download from iTunes Match.
This tip works with all iOS devices running iOS 6 or later.