well in my opinion...
wasn't the shy kind of guy
include yourself into things that you normally wouldn't do
EVEN IF YOU DONT KNOW WHAT TO DO DURING THAT MOMENT
ahaha XD
i guess i play for adventure
but if i look at it... the shyness hmm what could we do about that...
how fatal ( serious ) is your shyness
is it like... 8 or 10 (1-10 scale)
i'd probably ease up to an outgoing thing...
include yourself in school activities that have you talk alot infront of people
like right now, im part of " Asian Club " in my school, so i constantly have to talk to new faces about recruiting / school activities...
im starting our opener for tuesday's Open House, at night, so i have to introduce parents, support our club, and make us look good ( how nerve-wrecking )
but my point is,
slowly start to include yourself in outgoing areas
it'll show everyone that you're the sort of guy that wants to be noticed or the kind of person that is fun and you can count on, instead of lowering down to someone that is 50/50
now with the girl...
i'd probably ask her friends what she's into... music for example
look up some artists, check their songs...
if you like some, download em XD
ipod/zune/mp3 whatever
i play my music kinda high so people KNOW what im listening to...
-im not saying play your music high though-
but if you happen to like...
become physics buddies or lab buddies or something
open a topic with something like
" hey *wave* i like your hair "
something complimenting her?
could also try like...
" you know we've known eachother for awhile, but we've never really had the time to talk to eachother..."
personally, when im partnered up in any class, i try to get partnered with the person i least know,
so i can make a good impression that im not some low jerk that only gets to know people that i like, i can make the impression that i WANT to have as many friends as possible
talk to her, like you would talk to any of your friends... (in a self respecting way that is)
compliments are a plus...
music / movies / animes are good also, depending on the girl
oh another thing
FOOOOOOD
if she's korean, japanese, thai, viet, chinese, pinay(filipina), etc etc
bring up some good foods

my experience: Cantonese, Filipino, Japanese, Thai are the best... i wouldn't know what to recommend if my life depended on it! ahahaha XD
random topics are good +++
eheh, i doubt this would help but... its how i deal with things.
good luck