The 6 areas are ranked in increasing order of difficulty. The 6th, and hardest, isn't available until the other 5 are finished. I strongly suggest you attempt them in the given order.
 
Choose an area, and get a puzzle. Solving it allows you to move to the next puzzle, until they're all solved.You'll get a key at the end of each area: keep this.
 

 

Fire Path Metal World Water Way Sand Course Leaf Trail Crystal Glyph