Well, to be noticed you have to speak up. The squeaky wheel gets the grease!
Clean something that needs cleaning without being told to.
Chef, I finished that, what next?
Chef, could you show me how to make something you haven't made in a long time?
Chef, what do you think I need to learn?
Chef, would you consider letting me make the _______ by myself?
Chef, would you show me how you order in supplies?
Chef, how can I do this more efficiently/faster?
Chef, can you show me how you put together a menu for a special event. (New year, Easter, birthdays, etc.)
Chef, what should I read?
Chef, Chef, Chef!!!
Understand that you have to complete required work before asking these questions!
The chef should get the message you are there to learn and you will get noticed.