Write a treatment. Start with a rough draft that explores all the possibilities of your concept and don't worry about the length. Once you have all your ideas on paper, pick out what's most exciting and describe your concept in one to three pages. Keep it visual. Describe what your reader would actually see on the TV screen.
Create a log line. Imagine how the show would be advertised in a 30-second commercial. Summarize your concept in one or two sentences.
Register your work with the Writer's Guild of America. You don't have to be a member, but registration will cost a bit more if you're not. Though this is all the protection you're likely to need, you can also register with the U.S. Copyright Office, which also charges a fee.
Choose a submission platform. The Television Writers Vault is a reputable online resource for beginning TV writers and may be your best bet for scripted television, though networks and production companies often have ongoing contests for reality show ideas.