Where are the four beanstar pieces and how do you get them?

The locations are when they first go missing:

Teehee valley
Chucklehuck woods
Guffwha ruins
Harhaal's studio
After you go to these places to get the Beanstar pieces your path is pretty linear.

The first:
Teehee Valley, some Pirates find it and then they set sail with M+L on board. After they sink the piece floats to the surface, a Lagoon. To get it you must beat Hermie (the Hermit Crab).

The second:
Harshal's Studio, near the airport the famous fashion designer Harshal asks for help in trade for the Piece. To get it beat Harshal's fashion challenge.

The third:
Yoshi Theater, talk to Bubbles's younger brother (who is filthy rich). You must now go get all the Bean Fruit and feed it to the Yoshis to get 7 neon eggs. To get the piece give Bubbles's 7 neon eggs.

The last:
Chucklehuck, beat the colluseum and then enter the forbidden area. To get it beat Popple (Ya it's him again)

Bring all 4 pieces back to Queen Bean to get the next message from Bowletta!

1:The First Bean Star Piece is in TeeHee Valley,Where some pirate guys try to keep it for themselves.2:In ChuckleHuck Woods,use the fire rush move to knock down the giant koopa,then beat the colliseum.In the end, popple will battle you for the piece.3:In Harhall's Studio, beat her fashion challenge and she will pay you the third piece.4:In yoshi Theather,give 7 bean fruits and feed them to 7 hungry yoshis.then talk to the theather owner to get the last piece of the bean star.Then go to the beanbean castle to get the next message from Bowletta.