The easiest and most effective way to approach girls with out being rejected is to use an indirect opener.
An indirect opener telegraphs no interest to the girl your talking to which will then allow her to lower her guard and allow you to continue the conversation.
One of the most common used indirect openers is the opinion opener.
How it works is you ask a girl her opinion on something and it can really be anything.
The main key to your questions is that you want it to be an open ended question so that it strikes up some conversation between the two of you.
I would also recommend using a false time constraint when using an opinion opener.
A false time constraint is when you tell the girl you can't stay long.
When you tell the girl right away that you can't stay long this lowers her guard because she now knows right away she won't be stuck talking to you for hours.
Of course if the interaction is going well she will have no problems with you staying longer.
Here is an example of using a indirect opinion opener with a false time constraint.
You: Hey real quick I need a female opinion on something? Her: Sure You: Do you think it's wrong to break up with someone over the phone? Her: (She'll usually answer how long you've been together) You: Only a couple months but she lives in another city and I don't want to make a trip just to break up with her in person.
Her: (She'll answer) Depending on how she answers you can take the conversation in whatever direction you see fit.
So there you have it how to approach a girl without rejection, now get out there and start talking to some girls.