The most important thing to remember is that it takes time for a shy person to open up and feel comfortable around someone new.The key to dating a girl who is shy is simply to make her feel comfortable.
Let her know that you're the biggest goofball between the two of you.
This will make her feel comfortable because she'll be able to forget how shy she is and let go of any pressure she feels in trying to make conversations or worrying if she's making a fool of herself.
If you're not a person who is naturally goofy or outgoing, it's also helpful to just take your time and not notice or care about her awkwardness or shy tendencies.
Getting to know someone who is shy can be a frustrating experience, especially if you don't know the reasons why that particular person is shy.
In a dating situation you may read the signs wrong or not be able to judge if she is actually into you or interested.
I've always been a shy girl myself, so below is some very good advice that I would give to people who would want to date a shy girl, as well as what has worked (and what hasn't) when someone was dating me.
Before you even consider to date a shy girl or befriend her, it's important to understand that people are shy for their own reasons.
Some girls are shy because they have had a bad experience in the past, such as getting bullied for being the "know-it-all" in class while others learned from their parents to never talk unless spoken to.
Some girls are also more shy around boys, especially if they've never had someone interested in them before.
Knowing that there are multiple reasons to why people are shy will allow you to understand and be patient with the girl you're wanting to get to know (and potentially date).
Being too straightforward and pushing her to talk will only make her feel pressured and less likely to feel comfortable around you.