Apps will show on your Home Screens. To delete them tap and hold on an icon until they all start to jiggle, then tap the (x) in the top left corner of the app to delete it. You can also drag apps to reposition them, or to the edge of the screen to move them to different home screens.
Alternately, you can delete apps (and sometimes their contents) under Settings > General > Usage > Manage Storage (under the Storage header, not iCloud). Tap on the app in the list for options.
The build in apps can not be deleted, though their contents 'usually' can. Music can be deleted form here.
Music can also be deleted in the Music app. (instructions for iOS 8.4)
Gap on the My Music tab at the bottom. Choose Songs from the menu at the top center. Tap on the ... at the right of each song, and choose Delete. Or, if you use iTunes Match (don't know, then you're not using it) you could choose Remove Download. In the second case the song will still be available to play streaming (while online) but not stored locally (for play offline). Or maybe this is an option for the new Apple Music service (free trial for 3 months right now).
At the moment I'm signed up for both, though since iTune Match's features are included in Apple Music I probably won't be renewing iTunes Match (unless I decide for some unforeseen reason to cancel Apple Music after the free trial)
Note: Listening to Beats 1 station right now (Apple Music), just to get an idea of whether I'm going to like it.