This is really only a starting point - these are my recommendations for what to try, but there's so many music apps available and everyone uses them differently. Try out things that appeal and see what works for you!
Free, fun and easy
- Figure (free https://itunes.apple.com/us/app/figure-make-music-beats/id511269223?mt=8): Techno for everyone.
- Noiz (free http://studioamplify.com/noiz): The Too Much Not Enough theme was made in this! Really powerful but also fun and tactile.
- Blocs Wave (free https://ampifymusic.com/blocswave): Manipulate and combine premade loops however you like.
- Groovebox (free https://ampifymusic.com/groovebox): A synth and beat studio. Easy and powerful.
- Soundforest (free https://www.soundforestapp.com/): Create music sequences with woodland creatures.
More complex, more money
- KRFT (£14.99 http://studioamplify.com/krft): The upgraded version of Noiz. Create your own modular interfaces to play from live.
- Gadget (£19.99 https://www.korg.com/uk/products/software/korg_gadget/): This is expensive (especially when you get to the in-app purchases) but it's really a fully-fledged workstation for iPad. My most-used app. There's a free limited version you can try out.
- Beatmaker 2 (£11.99 https://itunes.apple.com/gb/app/beatmaker-2/id417020234?mt=8): A pretty powerful grid-based workstation; samplers, synths, drum machines, audio recording.
Fun and easy
- Pixitracker (£2.99 http://www.warmplace.ru/soft/pixitracker/): Fun, easy to use, actually pretty powerful. Good for retro stuff (16-bit version) and chiptune (1-bit version). The best tutorial is probably the one the guy who built it made: https://www.youtube.com/watch?v=mi9hg1tPlk0
- Nanoloop (£3.00 https://www.nanoloop.com/): Very limited, but very pleasing four-track sequencer. This is also available for Game Boy. A really good getting-started tutorial here: http://www.docpop.org/2014/05/nanoloop-tutorial-learn-how-to-make-a-song-in-30-minutes/
- Kaossilator (£8.00 https://www.korg.com/uk/products/software/korg_kaossilator_for_android/): Allows you to build up loops by moving a finger across the touchscreen.
- Caustic (£10.00, free demo on Android, https://play.google.com/store/apps/details?id=com.singlecellsoftware.caustic&hl=en_GB https://itunes.apple.com/gb/app/caustic/id775735447?mt=8): a fully-fledged, if quirky, workstation! There is an overview here https://www.youtube.com/watch?v=q86OrU-E7RU but each individual synth has (and needs) its own tutorial https://www.youtube.com/user/CausticApp/videos. It is capable of a LOT but accordingly it’s perhaps the most complex app I've listed here.
- FL Studio Mobile (£7.99, https://www.image-line.com/flstudiomobile/): The popular desktop workstation cut down for mobile devices.