Stars light up when mouse hovers
Simple, have an image for yellow star and an image for white star. When a star is hovered, all stars to the left have their "src"s changed to the yellow star, all stars to the right have their srcs changed to the white star.
Page isn't reloaded when star is clicked
Look into Ajax/XHR
http://en.wikipedia.org/wiki/Ajax_(programming)
Hint: Have a .php file called vote.php , and pass into it the ID of your food and the rating given by the user.
Some sort of average shown between the stars
Most websites only show 0%, 50%, and 100% stars... users won't really freak out if they don't get 'exact precision'
Rating should be stored in MySQL database
Any database system is fine. But yes, you would probably want to use an SQL database for this
