You must memorize your part to be prepared, but you also need to be familiar with the entire script to act in it effectively. If you thoroughly understand the story, then you have context for your character. Knowing the full context of your role allows you to build your character intelligently so that everything you do is in service to the story being told. A lot of actors read the entire script maybe once at the first cast read-through and after that focus on their lines. Reread the script repeatedly throughout the production's run so that you understand each story beat and what level of energy you need to bring to your scenes to keep the story on track.
Actors are often guilty of not effectively listening to their acting partners unless they are waiting for the next cue. This is a bad habit that can ruin scenes, because the audience will quickly grow bored watching actors who are not connecting with each other. There is a lot of truth to Spencer Tracy's advice that acting is largely reacting to the other person. Perform exercises with your acting partners in which the objective is to simply listen and wordlessly react while they talk. Staying in character when the other actors are the focal point not only makes them look better, it also enhances your own performance and helps create a believable scene.
Being tense prohibits you from effectively expressing your character's state of being. When you are tense, you cannot focus on character, your fellow actors or the scene itself. It's also a mistake to think that you have to be keyed up to play a tense character, because you certainly wouldn't get drunk to play a drunk scene. Before performing, you should practice some breathing exercises and stretch your body. Warming up is one of the simplest and most effective ways to relax your mind and body before performing so that you can concentrate on the work itself.