1. Read these two books:
What They Didn't Teach You in Graduate School: 199 Helpful Hints for Success in Your Academic Career , by Paul Gray and David Drew
How To Talk To Anyone, by Leil LowndesThe first book's title speaks for itself - it is basically insider information on the bizarre world of academia. It's short, sweet, and 100% spot-on, in my experience.
The second book is a How To guide for networking - I actually heard about it from an NSF program officer. It's not scientific or academic, and the author can be occasionally quite flakey in parts, but it's been my manual for interacting with people at conferences, talks, etc. I'm reasonably outgoing by nature, but when, say, I'm sharing the elevator with the Huge Famous Program Chair of Big Conference, it can be pretty intimidating. This book has really helped put me at ease in interacting with others.
2. Get comfortable talking to people about your research. Have a two sentence blurb ready-to-go about who you are and what you do. Haven't done anything yet? That's ok - just talk about how you're going to be extending your Advisor's work on X, and ask the other person about their research. (Everybody loves talking about themselves)
3. Get comfortable giving presentations. Everyone is scared when they start, not to worry. Take classes that help you practice. Your university/department likely offers classes on this, and if not, there's a ton of books/lectures/etc. (A few people have recommended Even A Geek Can Speak). But I highly recommend a class - it's just so incredibly useful and helpful.
4. Write Every Day. Every day, write a few paragraphs. Keep a text file, google doc, paper notebook, blog, whatever you like - but write down your thoughts each day. Read a paper? Write it down. Wrote some code? Document it. Tried a small experiment? Write down the results. If you write as you go along, writing your dissertation and/or academic papers is much less daunting.
4a. Get Writing Help If You Need It. When I was an undergraduate, I TA'd a humanities course in my minor, and invited my CS friends to take it to fulfill some of their general ed requirements. (I loved the course, so why wouldn't they?). These students were super, super smart thinkers, but their writing... oh my. Let's just say it left a lot to be desired. And they were native English speakers, so it wasn't that, it was just that they hadn't had a lot of formal instruction or practice. So again, take classes, attend seminars, whatever they offer - do it. Also, great book is: Writing For Computer Science, by Justin Zobel.
5. Your Advisor Isn't Your Everything - Build Your Network. Somehow, people get to graduate school and think their advisor is the only person in the world who is responsible for their education. This is incorrect. You are responsible for your education. Your advisor is only one of many people who will help contribute to this education. Go to talks. Send emails. Read blogs. Talk to people at conferences. You need to build up this huge cadre of people who you can go to when you get stuck. That way, if Person A is busy, you can ask Person B, and so on. Also, it's really nice to have a big mix of experts to talk to for specific questions - not just academics, everyone. I once got a great lead on a job because a friend of mine who shared a common hobby had a brother-in-law who worked there.
Ok, I think that's it for tonight (and sadly probably this week. So many deadlines!).