It's really easy when it comes to podcasts and audio books. All you have to do is tap the 2x button near the top right corner directly beneath the music slider. A screen shot is available below.
But what if it's a song that you want to change the playback speed for? Ok that's when it requires your computer. The process involves converting your song into a podcast.
1. Launch up iTunes on your computer whether it's a Mac or a PC.
2. Right click on the song or album or playlist... and choose 'Get info'
3. You might get a warning saying that 'Are you sure you want to edit information for multiple items?' Just click on 'Yes'.
4. A window will come up with 4 tabs at the top. Click on the tab that says 'Options'.
5. Change the media kind from Music to Podcast then click ok.
Now your song is saved as a podcast. You will need to re-sync your iPhone with iTunes whether wirelessly or with a cable. If you have wireless syncing set up then it should happen automatically overnight. Now when you launch your music or podcasts app you will find that your song is saved as a podcast. Just tap the 2x button and enjoy double speed! If you need any help, feel free to ask.