Begin by choosing a game and making recordings of yourself playing the game. This will help to familiarize you with the software you will be using when you actually make the machinima, but more importantly it will provide you with reference footage while you are writing. It will be crucial to understand the expressiveness of your chosen game. While you might be able to tell a soap opera using The Sims, you might be hard-pressed to do a retelling of Shakespeare with the NES Super Mario Bros.
Review the reference footage. Determine what the most interesting characters would be. Ideally, you want characters that you can control. Look for visually interesting characters and for particularly expressive characters.
Brainstorm character traits for the characters, situations for the characters and anything else which might be relevant to your idea. Decide whether this will be a "one-off," in other words whether you will make one short with these characters, or if this will become a series. This is also a good time to consider length. Remember that you had better have a good reason for making people sit through more than 5 minutes of video game footage.
Use the word processor to write your script. There are many choices for software which will automatically put it into script format, however, if you are making the movie, you really only need a script which you understand. Don't get too bogged down in the script details. If you understand that scripts have action, which describes what you see, and dialogue, which tells you what the characters say, you are ready to make your machinima script.