Yourself first, so you can better help educate others in the future. If you're new to abolition animal rights; I would suggest starting out with Making A Killing: The Political Economy of Animal Rights, by Bob Torres; followed closely with Animals as Persons: Essays on the Abolition of Animal Exploitation by Gary L. Francione.
Engage in a dialog
With your neighbor, best friend, the person ringing up the vegetable that asked you what it was and how you "use" it. Places NOT for this however, is at a table full of flesh and the like. And have literature on hand to give away for that unplanned conversation you got into because of your 'Animal Liberation' tee-shirt.
Bake and share
Seems silly and easy, but a few dozen cookies and brownies brought into work or a late night study group can work wonders. So many people think that veganism is about "giving up" all these things, and constantly give me this as reasons why they could never be vegan. Showing folks that there's nothing to give up is a great way to positively advocate for veganism.
Even if you just find time to do it an hour every other week, you can reach so much people. And if you bring friends and cookies, it's really not that hard at all. Vegan Outreach has some great ones, or just make your own.
Display info in public areas
The eco-savvy route of leafleting. Any place there is a public board--the library, coffee shop, co-op; put up an eye-catching little flier with information.
Focus on your strengths, and be creative
You know that thing that they teach us in kindergarten; everyone is good at something? Well, it's true, and you can use that to achieve the best form of advocacy. Whether it's painting, writing, baking, talking-- whatever you are good at; think of ways you can convert that into activism.