Hi moeburn
Make her feel comfortable around you. Make her feel a sense of security, make her feel that you are someone who she can trust. Best way is always stay calm and collected. Offer advice and help where you can (Even if it's emotional support) and most importantly be fun to be around. Have a sense of humour, make her smile. Do this and it won't be long until she warms up to you
Having said the above, you may need to prepare yourself for some emotional baggage. This girl sounds like she has been in negative situations that you have never experienced. Be ready to work through this with her...
Don't cry, don't regret and don't blame
Weak find the whip, willing find freedom
Towards the sun, carry your name
In warm hands you are given
Ask the wind for the way
Uncertainty's gone, your path will unravel
Accept all as it is and do not blame
God or the Devil
~Born to Live - Mavrik~