One important aspect of dialogue is learning to write and format it properly, especially in a story. Play a game where you distribute a written dialogue that is formatted incorrectly. After teaching students the rules surrounding quotation marks, punctuation and indentation, have them correct the dialogue and rewrite it properly. Alternatively, give students a paragraph of prose that describes a conversation taking place. Have students rewrite it in dialogue form.
You can help kids learn dialogue with games that make use of their creative writing skills. Show students a picture of two people engaged in some sort of action. Have them think about what they are talking about and write out a short dialogue. Ask students to come to the front of the room and read them. Ask the rest of the class to vote on the winner. Alternatively, have students write a dialogue for an imaginary situation, such as two people arguing over where to eat dinner, or even two animals engaged in a discussion.
True to the nature of dialogue, get students talking to one another in games that teach them dialogue. Break your class into pairs. Have each pair write a dramatic scene together of two people talking. Make sure they don't state explicitly what the scene is about. Have each pair act out their dialogue in front of the class. The rest of the class must guess what the scene is about.
Improv is a fun and effective way to teach young students about dialogue. Have two students come to the front of the room and mime actions together. Their actions can be totally random without a topic. Have two other students do a voice over, saying out loud what the two miming students are talking about. The game is fun for all and should get good laughs from the rest of the class. Another improv game involves having two students improvise a conversation about a topic that you give them. The one restriction is that they can only speak in questions. The first student to hesitate or say something that is not a question gets replaced by someone else.