Decide who the two characters will be in your scene. Will they be lovers, roommates or family members?
What do your characters want? Each must have something they want in order to build on the tensions in the dialogue. For instance, your characters might be two lovers who disagree on who is going to prepare dinner. Your characters' wants will determine the actions (the dialogue, in this case) they commit in the scene.
Create strategies for each character as they achieve their goal. For instance, one character might use guilt to get the other character to do what she wants. The other might be uncommunicative, rarely saying what he feels. These strategies help build the tension in the dialogue as each acts and reacts to what is being said or not being said.
Determine the subtext in your scene. Have characters discuss one thing while indirectly discussing something else entirely. For instance, the two lovers mentioned above could be having problems in their relationship. Perhaps one is consistently unemployed and this creates tensions in the relationship. An innocuous conversation about who will make dinner that night then becomes a much more serious conversation about the expectations one character has for the other and the other's incapacity or refusal to live up to them. Subtext alerts readers that something more important is happening here and adds tension to the dialogue.
Have each character try to maintain control in the scene through the dialogue. The need for either character to control the other adds more tension to the scene. The dialogue should reflect the shifting of gears as each character tries to dominate the conversation. This can be done by having one character interrupt the other or by using strong and forceful language. It can also be done indirectly, with one character answering the other in monosyllabic answers or answering questions with questions. As the dialogue moves forward, each character should attempt some strategy to maintain control over the conversation. Another way in which characters might maintain control is by refusing to say no.
Escalate tension in the dialogue by creating more obstacles for your characters. For instance, each time one character tries to resolve a problem, the other character creates another obstacle that prevents the former from resolving the conflict. In the example above, the girlfriend offers to go out shopping, but the boyfriend states it will be too late to make dinner by the time she returns. The girlfriend might suggest that he get started with dinner while she is out shopping, thus getting a head start, but the boyfriend might create another obstacle or change the subject entirely. As the boyfriend creates more obstacles, he makes it impossible for the girlfriend to resolve the conflict. The tension this creates should be reflected in the dialogue as each character grows more frustrated with the other.
As the tension escalates in the scene, the dialogue should reflect this tension. This can be done directly ("Dammit, why aren't you listening to me?") or it can be more subtle. The characters, depending on their personalities, can become more sarcastic ("Gee, and you wonder why I don't cook more often.") or snide. At this point, the dialogue should reflect the character's escalating emotional states. If the character is angry or hysterical, then the dialogue should reflect that by using more forceful and direct language.
End the scene by creating an event in the dialogue. An event can be anything that determines your character's desire to end or resolve the conflict.