1. Never link Facebook and Twitter together or visa versa. People using Twitter tend to want to view tweets and not URLS redirecting them to Facebook, because the text was too long to post. People on Facebook don't really want to see '@' mention signs that comes from a tweet.
2. Never update Facebook as often as you would Twitter. I was always told around 9 or 10 status updates a week for Facebook and no more than 14 Twitter updates in a day making sure you don't tweet more than once an hour. It's easy to be perceived as a spammer by over sharing.
3. Spread your posts over a week (if you have time) this will increase your engagement and reach.
4. Interact with your audience on both Twitter and Facebook, If someone responds to one of your status updates its good practice to acknowledge them. It keeps them interested and shows you are friendly.
5. Post a mixture of original and others content (retweets and shares), but remember to acknowledge who has produced it. Original content engages your audience and this can take the form of original thinking about someone else's work, e'g a review or response to a post you have read/watched or heard. Always remember to reference them.
6. Use photos with your posts that illustrate your point,
7. Think about your audience and what they would like to read, watch and hear, post content accordingly.
8. Read the statistical measurements that are available on Facebook Pages and Twitter, e.g. engagement and reach for each post and have fun experimenting with different content to see what happens.
9. Post different types of media, e.g video, audio, photo and written. Variety really does engage the audience.
The disclaimer, a few people who know me, may say that I don't always apply these points, and they are right. I think that it's about experimenting in your context (see point 8).