There is no magic pill. Mostly, it's a deep breath and "just do it" decision. Our mentors will encourage us. Our networks will support us. But, in the heat of the moment, it's just you and a big world full of strangers.
There are some terrific blogs out there on this topic - some with great perspective and some with checklists.
For large events, the blog Do the Work has a great post about meeting folks at professional events. My blog has covered the topic over many posts. Feel free to leave your favourites here for others.
But why start swimming at the deep end of the pool? You meet folks every day. Do you find yourself hiding in corners at work? Ducking behind the cereal displays at the store? Lurking behind a tree when someone walks down the street? <grin> You might even nod and say hi.
Try not to think of meeting strangers (or acquaintances) as something you only do at events. It's a daily practice and, like all well-cultivated habits, you can master it till you don't remember how not to smile and greet new faces.
I can write about how to do it till my keyboard wears out. You first need to simply decide you will try.