To unlock the Master Mode version of a song, you must score over 100,000 points and achieve the highest level for every phrase in the song. Use the song leveler if you don't have any phrases maxed. "Song" 2 and "Go With The Flow" are both fairly easy songs to master and memorize.
Once mastered, you will have to play the song in Master Mode. You can access the song from the Song menu and there will be an option to play in Master Mode in the arrangement you have mastered. Master Mode is different from regular mode in that you do not see the notes. You must play this from memory.
If you have a difficult time remembering a song, I highly suggest you try to sync it up with a YouTube version of the song played at its highest level. I achieved this by starting the YouTube video and pausing it on the third metronome click. Then start the game and on the third click, I hit play on YouTube and play along with that note highway.