Here are some advice from wikihow.com on how to ask a female friend out on a date:
1. Look for Signals that she likes you. Learn to read her body language. Is her affection towards you brotherly or potentially romantic?
2. Find out what her interests are. You have a better chance of scoring a date if you're inviting her to an activity or event that you already know she's interested in.
3. Wait for the right moment. Ask her out in person, but over the phone is also an acceptable option. DO NOT ask someone out over Facebook.
4. Be Clear. Whether you propose a trip to the movies or offer to cook her dinner, she might misinterpret your question as just a friendly gesture. Again, make it clear that this is a date.
You may read it from this link: http://www.wikihow.com/Ask-a-Female-Friend-out-on-a-Date