Memorize the line or action that denotes your entry into the scene, as well as your exit. These serve as your cues for scene entry and exit, according to ActortoActor.com.
Familiarize yourself with the overall story of the script, especially the scene and the lines that precede yours. This allows you to foster the appropriate responses and tone to work into your delivery.
Read the line or the lines preceding your first speaking point, as well as your first line. Have someone read you the cue before your entry and respond with your first line, trying not to read it, but recall it instead.
Review the next section of dialogue, paying the most attention to your own lines. Absorb the dialogue that does not belong to you as well, so you are aware of when your line is approaching. Have your assistant read you the other player's lines and try to repeat yours back from memory.
Start from the beginning of the script and try to recite from memory all of the lines you have reviewed up until that point, using the script cues spoken by your assistant.
Continue working through the dialogue, a section at a time, reading through both your lines and the other lines. Pay special attention to the cue lines that alert you that your line is next. Each time you learn a new section, go back and start from the beginning to review all of the past lines.
Put down the script and have your assistant go through the entire dialogue with you several times. Ask the assistant to correct you if you miss a line or say it incorrectly. Review that section again until you have it mastered and then continue to review the script as a whole.
Tape record your practice sessions, covering only your lines of the script, if an assistant is unavailable. Go through the entire dialogue, reading only the lines of the other players and reciting your own from memory. Play back your performance and concentrate on any sections that you stumbled through.