Posting here is a great start! I'm far from a professional designer, but I'll give my take on the subject as I've just gone through it (and still am).
Learning design is similar to learning a lot of skills these days. The key, to me, is to always learn more by creating projects and to get involved in a community doing the same. You can (and should to some extent) do these things offline, but doing them online is incredibly helpful because the whole world is at your fingertips! (Sorry for being cliche, but it's true, haha)
The simple fact is that you don't need a mentor because having many mentors is better. What I mean by that is there are fantastic communities online (and offline) where people learn and help teach about all sorts of things. The best I've found for most subjects is here on StackExchange, specifically GraphicDesign for design related things.
The community here on SE is open to anyone interested in learning more and is nice about it. Here on GD there are professionals in most all fields of design, from print to web. I get helped by a whole lot of the people on here, but can often help others given my background with the web and programming.
The Q&A is incredibly helpful for any specific questions you have and the chat is available for more general subjects, quick questions, and just general conversation with others. This can be more valuable than you might think. Often times I've been encouraged, gotten ideas and learned things I would've otherwise not learned by being a part of the chat.
By becoming involved in a community like this one, you can not only learn by asking question, but also learn from trying to solve other people's questions and reading (listening) other's conversations and interactions. This will help your ability to think well and solve problems past that of your own experience. Having people of all skill levels is also helpful because you can learn from those a little further along than you and, in turn, you can help others who are a little bit less further along.
It's also very nice because you see that everyone, professionals included, have troubles and questions. We help each other when we get stuck and give (perhaps too much of) our own time to help solve someone else's problem(s). We do this because we care, because others often help us, and because it helps us too.
Being involved in a community like this one not only improves your design skills, but also improves your ability to ask good questions and to work with others. Over the short couple of years I've been involved, I've gone from asking a good many somewhat poor questions to solving most of my own problems and only asking really good ones that I can't figure out the answer to.
I've also become a lot nicer in the way that I convey myself to others through text and how I handle others who don't always act courteously. It takes time and no one is perfect, but we all get better and better at what we do, from interacting with others to creating our work.
Of course, you can't become great at something if you don't do it. As such, you need to create work - and lots of it - to gain actual skill and build a portfolio. There is "the gap" between knowing what's good and creating what's good which takes a long time to overcome. But, with time and effort, you'll be able to do so before you even realize it :)
Always have a project (more likely projects) you're working on. Something that you really care about and enjoy working on. This will keep you learning and keep your interest for the subject. Plus it's fun! I love the whole process of thinking things out, building them, and looking back on the work I've done. It may be even worse than I remember it being, but it's something I created, something I'm proud of.
If you really do want a one-on-one mentor and the chats won't do for some reason (I really do think they're perfect for most people), try a local design school or studio and ask around. Most people are nice enough to help you every so often or to tell you that they don't have time to. It never hurts to ask! Just know that they are giving their time and don't be annoying about it. They may need a reminder every so often, but nothing makes me not want to help more than someone being annoying in the way that they ask.
There are also mentorship programs through groups like the AIGA (American Institute of Graphic Arts), linked by Ryan's answer, which can be found and are created specifically for this purpose.
A lot of these thoughts, along with others, can be found in my blog post Why I Still Contribute to StackOverflow. I think it's worth a read :)