Prepare a thorough set of documents regarding the series. Often called the show's bible, this includes a one-page treatment (summary), the pilot script, character descriptions and descriptions of at least six additional episodes.
Find an agent, manager or producer willing to support your series idea. Independent producers tend to be the easiest people to reach. When a producer is willing to back your series idea, the studios take on less risk.
Practice the pitch. Keep the pitch less than 10 minutes. Spend a fair amount of time discussing the aspects of the series the studio finds most interesting. Be prepared to talk about the characters, plots or long-term vision of the series. Let the studio representative direct the course of the conversation.
Be flexible. Thank the studio representatives for their input. Compliment their ideas. You don't have to use every single idea they suggest, but be willing to adapt your script to fit an idea they might have. If you aren't willing to adapt, another writer will.
Don't try to control the meeting. Unless you have a lot of experience with studio executives, your agent, manager or producer will be with you. Let someone else decide when the meeting is done. Don't expect an answer at the meeting. In fact, studio executives rarely say no -- they simply don't say yes.