My stepdaughter went through this phase a couple of years ago. But, it wasn't so much that she was picky, it was more a matter of she wanted junk food over healthy food. When she would sit down at the table for a meal, she would pick at the food and play with it. Then when everyone else was done, she wanted down from the table. We would let her down, but put her plate in the fridge. When she would mention she was hungry, her plate was warmed up and put back in front of her. After a few times of doing this, she learned that she had to eat what was cooked before she got any type of sweets. She is now almost 5 years old and we hardly ever have a problem with her eating anymore.
Also, I read somewhere that it can take 8-15 exposures to a food before a toddler will start liking some foods. So we never give up on things she won't eat, until we have reached that 15 exposure mark. There were things that she wouldn't eat a year ago, that she will eat now; because we kept exposing her to them.