The only thing required to get ballot access in NH is to file a simple declaration of constitutional qualification, and pay the filing fee. The filing fee is $1,000.
I'm referring to a NH government instruction sheet (link there to NH Sec of State website, short PDF), last updated January 2011.
Thanks, guys, for the links and info. If I’m understanding correctly from combining your links, she would be required to have a federally registered presidential campaign committee only if she had received $5,000 in contributions to her campaign. At that point, it would be required that she file a statement of candidacy and register the campaign committee with the FEC.
Assuming she wanted to fly completely under the radar, she could conceivably let no one know, and have not accepted any campaign donations, then she could simply file her declaration with the NH Secretary of State and pay the filing fee.
If she chose option #2, it probably wouldn’t take more than a few days prior to the filing deadline to make sure everything went through okay prior to the deadline. If I was watching her like a hawk, as politico and others apparently are, it looks like they might have only a few days advance notice prior to the NH filing deadline, provided they have access to NH Secretary of State’s filings of declarations. I’d assume that’s public domain.