I cannot state this strongly enough. Voting is absolutely critical to the formation of a healthy SE site. And this is never more true than in Private and early Public beta.
Vote on Questions
Voting allows the community to determine what topics are allowed and what are not. Voting shows what constitutes a well-formed question and what is unacceptable for this community.
If you need help formulating better questions, the blog post Asking Better Questions might help you out. (Admittedly, it's geared towards the Stackoverflow crowd, but the philosophies there will help). Also, How to Ask directly from StackOverflow is an excellent resource.
Finally, I want to reiterate that Voting on questions is free! It doesn't cost you any reputation to to vote a question down. (Compared to answers:)
Vote on Answers
Voting on answers allows a dramatic increase in reputation. Like questions, it shows that you believe and support the answer provided. Also, vote answers up that you think are well worded and support the answer given.
You don't have to agree with an answer to vote it up!
To show that this is true, they've even created a badge for voting up competing answers (called "Sportsmanship").
If you think an answer is useful, vote it up. If you think an answer is not useful, vote it down. Either way, vote!
If you need help on writing answers, the meta post How do I write a good answer to a question? will help you out.
If people do not vote, there won't be enough reputation on this site for it to be promoted. Reputation is very important to a StackExchange site as it creates the groups of people capable of maintaining the site.
To show how critical it is, Jeff Atwood posted a blog article regarding this topic: Vote Early, Vote Often
Encourage others to vote!
Quoting RobertCartaino from chat:
Vote, vote, vote. Encourage others to vote, vote, vote. On good content, leave signposts ("If you like this, please vote it up. It's important for the community!")-- in both meta and the main site. Maybe a few meta posts informing the users of the important of that type of participation. You are empowered a lot more than you know.
This is a reproduction of a moderator's (Richard) excellent post on meta.hermeneutics.SE.