How to display certain select field options based on previous select box selection

How to display certain select field options based on previous select box selection

I have a form that has four select boxes. How can I set it up so that the selection from box #1 affects what displays in box #2? Then the selection in box #2 affects what options display in box #3 and so forth?

Example:
Select box #1 options:
- Green
- Red
- Yellow

Select box #2 options:
- Grapes (only shows up if "Green" is selected)
- Watermelon (only shows up if "Green" is selected)
- Apples (only shows up if "Red" is selected)
- Cherries (only shows up if "Red" is selected)
- Bananas (only shows up if "Yellow" is selected)
- Lemons (only shows up if "Yellow" is selected)