Make sure that you totally freak out and scream and all that before you meet them to get it out of your system so you don't end up looking like you're having a hysteria when you finally meet them.
To be extra sweet, why not make or pick up a cute gift to give them with a little card expressing how much they inspire you or make you happy.
When you actually meet them in person, feel free to ask any appropriate questions and make sure to take a few pictures as a memoir. DO NOT grin like a madman or lunge into a fit of nervous giggles as you will make them feel extremely awkward and uncomfortable and you will therefore seem like a typical, irritating fangirl.
I suggest you don't dress like you're going to be a star on the red carpet but also don't dress like you're going out for a morning jog. Jeans and a cute tee should be fine.
comment any other suggestions and I'll add them to the chapter x