Contrary to popular believe women are actually generally friendly when you approach them. A simple gesture like a smile can really break the ice and enable you to get the conversation going. As long as you're not rude and insensitive in general you will have a good experience.
I know that may seem out there right now but understand that women are not monsters and they like you want to be in a fulfilling relationship. Granted there is nothing worse than being rejected in front of others but you can look for signals in order to prevent this from happening.
Such as mentioned a simple smile and a "hi" can break the ice before committing yourself to an indebt conversation. If she says nothing, so what – at least you now know where you stand and do not have to take it any further.
This is better than trying to come up with some cheesy chat up line and being told go to hell. The key is to take the first step and each step after that gets easier and easier.
Women appreciate guys who have the nuts to take action. This they find attractive as it reflects confidence. This with a little intelligence and mysteriousness can really work in your favor.
When first chatting with her take note of her body language. If her posture is open and engaged then its OK to keep the conversation going if it is the opposite then see if you can pick up on something that she is interested in – if not save yourself the hassle and move on.
Have a little fun and take the edge off. Give her a hard time. Inject a little humor and be playful. Women really enjoy this. Do not get personal and listen carefully so that you can pick up on additional conversation wedges. Always be yourself and do not try and put on a show.
Women can see right through it as they get approached frequently and see common patters evolve. Get her to do most of the talking than slowly work your way in. Before you know it she will be comfortable giving you her number.