How to approach a girl without being random or awkward?

i really like this girl i see in the hall and cafeteria when waiting for the buss. i don't know her name because i have never talked to her at all. I'm in the 7 grade and i think she is in the 8th grade. ( I would have been in 8th grade but i had been home schooled from kindergarten to 2nd grade. and when i tried to go to 3rd grade for public schooling, the district held me back for a grade because of that and im now stuck in a grade lower). She is a very beautiful brunette girl and every time i see her, she looks like a really nice person. I am a very sensitive guy and im really nice and generous and sweet. I love alternative rock and especially acoustic music when im in a very emotional mood. ( i remember i listened to this really beautiful song about loving somebody no matter what and it touched me so much that i have the song stuck in my head which is your guardian angel by the red jumpsuit Apparatus). I really want to go out with her but im really really shy and there has always been a issue i have had which harms me really bad which is the fact that i cannot start a conversation very well at all. when i talk to girls, i start to hesitant and flem in my throat starts to thicken to where it is harder to talk in a normal fashion and i usually don't know what to say when try to talk to a girl and i tempt me be random and studder out of nervousness. like, i would ask them something and they answer and i don't know what else to ask her or talk about like,"hi, hows your day?" or , "hi, how are you today?" and something like that and when when they answer, everything goes silent and awkward. also when when something unexpected or something awkward or confusing happens, i tempt to have have strange body language and doing things without thinking and automatically doing something which actually looks weird. im always afraid things would not go right and i may give her the wrong impression or humiliate myself. i really need some help because i really really really like this girl and i really want to have everything go alright for sometime. PLEASE HELP ME AND I WILL THANK U ALL FOR YOU HELP. GOD BLESS YOU ALL!!!!!!!! :D