Being a newbie at this I hope my insights are helpful to others.
I have been seriously studying facebook marketing and currently have this page.
The way I built up the audience engagement is
1) first get 1000 likes at $0.05 per like with facebook advertisement
2) use tools like mpsocial to mass join groups that are related to my niche.
Once in, I start engaging MANUALLY. Many groups have strict rules about what can and cannot be posted.
3) I analyse the groups I am in and see what posts the people like
4) I go out and create the content. Emulate. So eg if there is a quote that gets lots of like and it is 300 days old then I go find a new image and quote with the website branded and post to the group. This way I know it has been liked and will likely have a chance to then be liked more.
5) rinse and repeat with as many groups as you like
Bonus method for for growing your page.
Repeat the above process for fanpages. The difference is that you do it in commenting as many fanpages don't automatically allow post.
So learn the culture of the pages you are visiting, watch what others do and then experiment.
I know these are basic and can be time intensive but the payoff is great longer term and you won't get put in facebook jail or offend other people.
Bonus bonus technique
Reach out to influencers, i.e fanpage owners or group owners and start a conversation.
Thank them for their time and effort (it takes lots to keep a group going)
Then politely ask if they would be interested in giving feedback on your page. Note: this is not asking them to promote your page.
It is a very subtle difference, one they look at your page and suggest changes, make them, then go back and see what they say.
If you do a good job with their suggestion they will like it and then you can ask for the promotion.
But wait there is more!
Bonus x 4 method in getting more exposure to your fanpages
Notice how the top method was in bullet point and it was much easier to read?
Here is what you do
Experiment with bullets
formatting makes a huge difference in engagement
always keep the readers perspective in mind
Hope that was helpful! I'm excited
"I'm in for the Giveaway"