For me, I have two methods.
For comedy skits, I will think of an idea that actually made me laugh out loud. Then I will research the internet (mainly YouTube) to see if anyone has already done my idea, and if they have, see if there is a way I can change it to still be original (although usually I will toss the idea and find a new one.) If original, I will come up with a plot for the skit, then write the script for it.
For more serious ideas like the webseries we are working on now, I will think of an idea that I like, check for originality, and then I will research as much as I can about anything related to this idea be it space, medieval, aliens, etc. I will then come up with names for my characters by either thinking of a word that best describes them, looking through a thesaurus, and then altering that word to be original and sound cool (or at least fit the character.) If there are a lot of characters, this can be one of the most tedious tasks for me since I seem to never be happy with names. After all this, I will begin writing general ideas down of the story (very rough at first) and then the more I think of it the more I refine the story to what I want. NOTE: Especially with webseries or longer stories, I feel it is important to be able to answer any questions you can come up with about your story. This way you will find holes in your story of things that do not make sense very quickly. If I can strongly answer all of my questions, then I will finally share my story with a friend, and then answer all of their questions until I have a solid story ready for an audience.
Hope that helped.