Platform is central to an agent's and editor's decision to take on a nonfiction project. When you query with nonfiction, it's OK to use up to half of the letter (about 250 words) with discussion of your platform--whereas with fiction we expect about two sentences (20 words) of author background.
The most effective breakdown I've ever seen of nonfiction platform (here) is into its external and internal components. 1. Why you? and 2. Who already cares?
Question one is about you and your past. Your resume. Are you an expert? How long have you been involved in this area? Who has recognized or employed you because of your expertise? Have you taught? Where have you presented or been interviewed? Your local newspaper in Small Town, Indiana is, unfortunately, not a viable element of this section of your self-pitch. The answers to this question have to be immediately recognizable to the reader.
Also evaluated with question 1: Can you write? Your pitch letter (which, as I've said, should include an overview of your platform) has to be compelling. You should convince me you're answering a question I have--even if I didn't know I had it before reading your pitch.
Question two: Who already cares? is about audience. The one you've already got slathering at your heels. It's not enough to assure the agent that you will gain x number of Twitter followers or implement such-and-such plan. Anything that refers to the future, unless it's something you've already been slated to do (I will appear on Good Morning America on this date!!), it doesn't constitute platform. It's too speculative.
If you speak to 50,000 people a year in x number of invited speaking engagements, that's platform. If you have a mailing list of 2,000 (the more the merrier, of course). If your radio show has weekly listeners in the top 5 markets--or, if you're on internet radio, the metrics will be different (by the way, Internet radio is getting big. You should look into it.). Where have your articles been published?
The bottom line: it's numbers.
Twitter is an insanely useful tool for building an audience and connecting with people who will publish or feature you. More than it is a social network, as originally billed, Twitter is an information amplifier. You tweet, someone retweets, an just because of these two actions your link or tidbit could be, theoretically, reaching thousands. Becoming a follower is a low-investment action. All you have to do is be useful once to get someone to follow.
So if you're an expert in an area, start Tweeting about it first. Link to already-established blogs. If you've driven enough traffic to them, perhaps you could apply for a guest-post spot on grounds that you'll bring readers--that you already have done so.
Bit.ly is a link shortener that also counts clicks. So you can see, out of the total number of clicks a link got throughout the whole internet, how many came from you. It can be compelling data. It could get you published. It could get you platform.
How have you gone about starting a platform? Anyone succeeded in gaining the numerical swag to start querying a nonfiction project?