I've always been kind of shy around people I don't know at all, so it has never been too particularly easy for me to meet new people (whether women or otherwise). For the most part, I think I have the other issues that accompany my shyness handled at this point, but the main issue with which I'm still experiencing difficulty is starting off a conversation with someone. I'm fine once I get past that point, but initially meeting people has often been terrifying for me.

While on the one hand I suppose this question could be phrased more generically to include people in general, and not specifically in regards women and dating, on the other hand I thought the answer might be different with women, dating, etc., or more casually, simply attempting to meet women without per se any initial intentions to date in mind until after I know them better.

Basically, in the past when I have asked others how one begins a conversation smoothly with someone they don't know, most commonly I am told a simple "hi" is usually all that's needed, and things should flow from there. This seems like a good idea, but do I have to be in eye contact with the person? Is it okay to say hi if she's not looking directly at me?

Ah yes, and for clarity, I ask this because it's hard to catch a moment where she's looking at me and I'm looking at her at the same time. I mean, I could just look at her and wait until she looks at me, but that feels kind of creepy to just be staring at her waiting for her to look back...