A lot of good advice. I'm also a female introvert. I'd also suggest reading "The Introvert Advantage". It really gives you a good understanding of introverts even if you are not one. There is some scientific explanation to the way we process information which is different to most people. Apparently, introverts are in the minority and for years they were viewed as "socially inept" or socially "challenged" by those who didn't understand the inner workings of introverted people. It was truly viewed as a weakness, which was rather unfair in my opinion. A dear friend of mine (also a fellow introvert) recommended the book to me and when I read it, it was like the light was turned on. I totally understood where I was coming from and why I definitely wasn't like most people I knew. I fit the bill almost perfectly and tested on the high end of being an introvert. So... I really recommend it. It might help you understand any future introverted girlfriends.
As someone else mentioned, introverts also aren't always necessarily shy, but can appear to be so to others. (I was shy as a little girl, though.) I think they appear like this because many don't feel comfortable doing small talk and don't feel comfortable around large groups of people. They are the ones at a crowded function who will usually find a small duo, trio or quartet of people with common interests and stick together for the rest of the night. I remember when my husband and I were dating, he'd take me to these get-togethers with the other graduate students from his department and he originally just thought I was either severely shy or just didn't want to talk to people and couldn't understand what was wrong. I was neither, but I also was very uncomfortable being around people I didn't really know and couldn't find anything in common with. I truly did not know and did not understand the art of small talk back then. It was painful and I'm sure people either thought I was painfully shy or was a snob. (It's so funny with a few good friends of mine who thought that originally of me before they got to know me. They thought because I didn't talk much I was a snob and then realized later that I wasn't.) I think through my training as a journalist in college, I also learned how to redirect any conversation with people by being the listener and the questioner, thus allowing myself to not have to really engage in small-talk and steered towards something interesting that both parties involved would enjoy.
In terms to what kind of men introverted girls look for, I can only speak for myself. I was interested in both introverts and extroverts when I was dating, but I tended to prefer introverts. I just wanted someone who understood me and accepted me for who I was instead of trying to "help me come out of my shell". There was no shell to come out of. My husband is actually an introvert, although not as much as me. He was this serious, brooding, intense, passionate young man, yet at the same time had this funny, dorky sense of humor which I absolutely loved and helped bring me out and become much less serious. I'm so thankful for that because I feel more balanced in life now.
My husband and I were friends for a couple of years before we began dating, but one of the first things he told me when we became an item was that we could go as slow as I wanted and I really loved that. (That said, I was the one who took the lead of allowing us to become an item. I knew that he wouldn't make a move unless I did since I turned him down originally two years before. So, I had to be bold. Something (God) was telling me to say something or I'd lose my chance.) Our dates usually consisted of quiet walks in the woods, gardens, to the museums, attending classical music concerts (we're both musicians - I'm now a professional and he did it for the love of it), drives out to the country, reading 19th century novels and discussing them.... I got him to read "Jane Eyre" and it inspired him to compose a song for me with text from the novel... and lots of talking about life and the world around us. I remember we'd sometimes really depress ourselves because we tended to carry the weight of world on our shoulders (something introverts tend to do) but then we'd have a lot of laughter and goofiness as well.