There are many ways to spur growth in a forum, and you'll find different sites using different tactics.  For example, some track your IP address and allow you to browse around a forum and view only a limited number of posts until you are then required to login (or signup if you don't have an account) to continue browsing and reading posts.  This is surely one way to grow your user base, especially when it's a forum for a niche topic where a lot of users land on from search engines or are looking for information on a certain topic, i.e. a car forum.  You can also do without the posts limit for non-registered users, and instead only have certain features such as viewing attachments such as images by first logging in.  Though these two tactics won't really spur engagement, it'll help grow the user base.  Though you must be careful because this might have an adverse affect and turn users away and have them not come back, because account registration is always a major roadblock as people are not very willing to go through a registration process unless there is an absolute reason.  So if the content in your forum is highly engaging, i.e. lots of posts and responses, then a user is more likely to register and join in on the conversation.

One way to spur the engagement amongst registered users is to offer incentives.  'Game theory' as it is referred to, where users receive badges or tags that they can showcase within their profiles for meeting certain milestones as far as activity (i.e. forum posts and responses).  As a form of bragging rights, this is definitely one way a lot of forums use to incentivize activity and spur growth within the forum community.

As far as getting the users to read a forum, you could do things like send period emails like "hey, we haven't heard from you in a while, check out these recent posts you might be interested in reading."  Of course, this would be an opt-out email, but it's a good way to refresh registered users' memory about your forum and the interesting topics posted in it everyday.

And of course, the larger the community, and the more interesting the content within the forum, the easier it is to get more users and more content.  Though then it becomes a chicken and egg discussion.  Start out with a nicely designed, simple forum, and slowly work on building content and users and adding features as you go.  Hope this helps!