It is very difficult to see a shy guy approach a girl they like. This is not just because they fear rejection but because they do not know how to approach a stranger and start up a conversation. You are shy, that is the first problem and this problem need to be solved first.
Now as a shy guy, you can learn to be more comfortable by breaking out of that shyness and learning to initiate a conversation with people. Engage strangers and comment on things to start up conversation. Join groups and butt into discussions. This help build your confidence levels. You don't have to talk to just girls. The focus is overcoming shyness and making you comfortable. Getting comfortable with people will help reduce the fear of rejection.
Learn to make eye contact. This is something shy people avoid but eye contact hdlps build a level of confidence. When you are talking to people, learn to smile and maintain some form of eye contact.
Once your self esteem has been boosted a little then you can approach the girl like but timing is everything. Approach her at a time when she isn't busy or angry or looking sad. Make sure she's free and happy maybe in the midst of people. That could be a Good time to approach her.
Make eye contact when introducing yourself and wear your best smile. Have a conversation starter ready to avoid the awkward silence that follows after introduction. It's okay to be a bit nervous and it is okay to mention it to her that you are a bit nervous talking to her. Compliment her and ask questions about her. This will help her relax and understand you realy want to know about her.
Before all these , looking good is advisable. Dress good and smart, wear nice cologne and be well groomed. Appearance helps to boost your self confidence also.