To shyflirt, or flirt if you're shy, you first have to own your shyness.
When you are actually confident in your shyness, it becomes a strength, not a weakness, and can be kind of cute. When you are shy, you are seen as less dangerous and people get comfortable around you quicker. So you can come up with a line like, "I'm really shy, but you seemed like a really open person. What's up?" Try that line to open. I think you'll be flirting in no time.
After the opening line, flirting gets much easier, but it still might be difficult for someone who hasn't had many conversations.
So, still owning your shyness, let the other person do most of the talking. Your job is to ask questions. Other people want to talk about themselves anyway, and you have again turned your shyness into a strength.
As they talk, you, in the shy passive position, now are actually in control.
You can take and give your attention as you please, and let them know you're really into them by body language, or that you're turned off by simply turning away or starting a new conversation. Body language is the most powerful form of communication anyway, so you'll be speaking volumes.
As you flirt with your body language, you can also lead with your body.
Like if you want some punch, all it will take is a shoulder movement towards the snack table. Because you are seemingly a captive audience, your flirt performer will do everything in his or her power to keep you happy and connected, so they will pay very close attention to your signals, and that's what you want.
If you do your job correctly, and you approach only people you like, they'll take the lead and ask for your contact information.
And there you have it, how to flirt even if you're shy. Good luck!