1. Write as though no one will ever read it.
When you sit down to write, tell yourself that you are writing for no one. Pretend that no one else will ever read what you are writing. Lie to yourself and tap into your inner thoughts, feelings, and fears. It is difficult to express yourself when you are constantly worried about whether you will lose friends or if people will suddenly hate you for what you write. You need to be able to toss those insecurities aside and write. Life is too short to hold back your creative genius just because a few stiff farts have forgotten that life doesn't revolve around them.
2. Write under a pen name.
Writing under pen names is a freeing experience. It eliminates the fear of being ostracized for your beliefs and deepest fears. I currently write under 4 different names. Each name has a different voice and I am able to write under a different genre for each name. There is no better way to give up your writing inhibitions than to publish your voice under a fictitious name.
3. Write as much and as often as you can.
Sounds stupid, but it's true. The more you write, the safer your writer's voice begins to feel. It starts to poke its head around the door and, with time, it gets out to exercise itself. The more you write, the stronger your writer's voice will become.
4. Read as much or as often as you can.
The best writer's have the most distinctive writer's voice. Harlan Ellison, Jane Austin, and Mark Twain all have a very distinct voice when they write. Read as much as you can. Study each voice, learn about each author, and even test out each voice in your own writing.