Stars are gained by playing through Adventure mode and completing specific objectives. Examples are: Score a certain number of points, use a special letter on the board, or create words with 3 letters.
3 Stars are possible from each puzzle, though for the most part you only need 1 star to move on to the next puzzle. Tap the Maps button in the upper right to choose between Adventure Maps and Extra Maps; Stars gained in either section will still count towards your 100 Star total.
Progress can be checked by clicking Menu, then Awards.
You will earn this achievement on your way to