Decide if you want your skit to be dramatic or funny.
Create two or more characters that are different from each other.
Place the characters in a setting or situation that causes conflict. Conflict is the driver of a story and is a main motivator in why people take action.
Write how each of the different characters reacts to the conflict and how they respond to one another. Do they work together? Bicker? Ignore one another? Are they aware of the conflict or are they oblivious? Your skit does not need to show the resolution of the conflict. It only needs to be a short scene with entertaining or interesting action or dialogue.
Create or decide upon a story that has a beginning, middle and end.
Choose the characters that must be involved in the story.
Make a list of all of the scenes you think need to be included to tell the story effectively. This is your scene breakdown.
Go through your scene breakdown and begin fleshing out each scene, including the setting and the characters that are involved.
Using the fleshed-out scene breakdown, go through and begin writing each individual scene.
Review what you've written. Whether you've written a short skit or a long play, you'll need to revise your writing. Remove all dialogue that is unnecessary, meaning it either doesn't add humor, reveal character or move the story forward in any way.
Delete entire scenes from a play if the scene seems superfluous or doesn't move the story forward in any way.
Do a read-through of the skit or play to hear what works and doesn't work, and to determine if the length is appropriate. Most plays should run up to two hours in length, so if your play is much longer, you'll need to delete scenes and dialogue.