Combine both objective and subjective drama. Suspenseful storytelling involves both scenes that are suspenseful because of the objective situation -- for example, a man trying to flee an ax murderer -- and scenes that are objectively suspenseful based on the audience's knowledge of a character, such as a man trying to overcome his fear of dogs to rescue his child's puppy. Too much reliance on objective tension makes it difficult to sustain suspense as the audience is unlikely to care about the characters, while too much subjective tension keeps the audience from anticipating real danger -- a key element of suspense.
Use uncertainty as a tool. The more the audience hopes for one outcome but fears for another, the more compelling your story is. Foreshadow what potentially may happen to a character as well as what could go wrong, and keep both outcomes appearing equally likely to build suspense.
Reveal information in the screenplay to your audience that your main character or other characters are not privy to. Using dramatic irony to convey information that the audience knows but the character doesn't builds suspense as the audience waits to see what will happen when the character finds out.
Plant elements of the future throughout the story. Small scenes that allude to future events build suspense slowly as the audience expects those events to occur. The payoff of planting this information early is that element of suspense as the audience waits to see how the planned event will go.
Develop a primary question for each scene, sequence and your screenplay. If each scene, sequence and your overall story can be summarized with a question, such as "Will Romeo get to Juliet in time?" or "Will Dorothy return home?" your screenplay will have suspense as you develop the scenes, sequences and story to answer that question.