Student screenwriters are often taught to take scenes they've written and chop off the first part and the last part. What's left is the middle, the heart of the scene, and the only part of the scene that remains in the screenplay.
What this means to actors is that you must start every scene as if you were "in the middle of things." Know what happens before the scene takes place that brings you physically and emotionally to the moment of starting the scene. Most of the time it won't be laid out in the script so it's up to you to decide. Have fun with it. Let your imagination run wild creating the circumstances that happened before the scene. It's your secret. You don't have to tell the casting director, director, or writer what you've thought up. All that matters is that you've created a "before" which is compelling for you and which you can connect with personally. It should get you from 0 to 60, so that you can start the scene at 60. Nobody wants to watch you warm up when you start the scene. You need to already be THERE! And your BEFORE will help get you there.
And life doesn't end with the last line of the scene either. Something always comes after. What is that? What does your character expect will happen after the scene and how does that color you in the scene? Again, it's your secret. But make it something that you can connect with in a compelling way.
The "before" and "after" can really bring dimension to the scene and bring it to life.