It's okay to be shy and flirt! If you feel silly then maybe tone it down a little. Flirting doesn't necessarily mean you have to touch their arm during conversation or anything too forward. It can be as simple as accidentally-on-purpose winking one eye at them when you laugh, circling a finger round the rim of your wine glass, holding their gaze just a fraction of a second longer than you might otherwise, or speaking a little softer so they have to lean in closer to listen. Just be friendly and interested in what they have to say. Most of all be yourself and you'll be fine. Good Luck!

I have the same problem! I am horribly shy around guys because of going to a single sex school for so long! However, there is hope! It doesn't have to be hardcore/very obvious flirtation. You can just smile and make eye contact longer than you normally would. Another way is through body language. Focus on their lips and eyes [called triangulation-or so I've heard]. Laughing and joking is always a huge plus [in my humble opinion]. Also compliments if you feel so bold. But really if you just seem genuinely interested and not like it's an act to win them over you should be fine. Just be genuine and it goes a long way. Good luck, and I hope it helps!