In the Music app do the following:
1. Select Playlists.
2. In the upper right corner click the "New" button.
3. Provide a name for the new playlist.
4. Add songs by clicking their respective "+" button to the right of their title. This bit can be daunting if you have a large library as the only navigation aid seems to be the alphabet on the right edge of the screen.
5. Click "Done".
Hope this helps.