Hello, I fully understand the situation you currently find yourself in. I am quite the same way inclined, very shy/reserved and often struggle to find ways to approach a girl. Conclusively, I personally do not think there is any hard or fast rules to approaching girls. Additionally, I think that if your going to approach a girl, its best said, to do so on your own. Because at the end of the day, you could approach her with your friends initially, but, ultimately it is you that is going to have to meet her from there onwards.
Now I am no expert, I am shy like you, and so in regards to my situation I have yet to actually approach a girl myself as such. As I have never actually, shall I put it, successfully approached girls. So I suppose in a sense, I could really do with taking a leaf out of my own book! But hey, I'm just here to point you in the right direction. In terms of myself, I basically just focus on some other aspect in my life, most notably my education. I have confidence in the fact that, if I focus on this rather than girls, life becomes much easier and more manageable. Therefore I feel less emotional and empty inside as such, its all about distractions of the mind.
Plus, if you focus on your education, or something of benefit, in the future you will be more equipped in terms of finance with a adequate career and so girls will be more accepting of you. Or even hobbies? You may well meet plenty of females which match your interests and you could find yourself a female counterpart!
Good luck and I hope my answer has provided you with some clarity and reflection. If you want to talk further PM me, all the best.