I think they don't disclose the specifics. The most detailed thing I found is a 1hr podcast. The most "technical" bits are mentioned about half-way through, but still pretty vague in terms of tech. The core of their tech is
discourse analysis software -- fairly vaguely presented in the talk
a network of influencers with which to fight back, which are often paid; pay seems to depend on how successful they are
At one point in the podcast a Vanity Fair article is mentioned, which is probably this one, basically giving roughly the same info as the podcast:
In Nevada Hougland’s team rolled out its plan to fight disinformation on the internet: an influencer-driven campaign from the left, rooted in facts but powered by the kind of personalized, high-wattage arguments that resonate on social media. The effort was decentralized, putting the message in the hands of social media “creators” in Nevada with large followings, instead of cautious Democratic strategists. “It stands to reason that a more personal, visually compelling message or video from a friend or neighbor is more impactful than another manufactured campaign email that’s gone through 17 layers of approval,” Hougland told me. Using artificial intelligence capable of analyzing tens of millions of online impressions daily, his team hunted for signals that human networks and bot networks on the right were using similar language, an indicator that certain gun narratives were snowballing. It geofenced the state and looked at 34 million expressions of attitudes around gun violence and gun safety. The algorithm would determine which language patterns were driving virality. “The machine tells you what language is most likely to succeed among different audiences in the movable middle,” he said. It turned out that Nevadans disproportionately viewed gun violence and gun safety as a health issue.
But instead of handing its learnings over to a campaign consultant to be made into a focus-grouped television ad, Hougland’s team mimicked what any competent brand or company does every day in the attention marketplace. It created an influencer-marketing campaign—politics for the Kardashian era. In the same way companies like L’Oréal or Budweiser approach and often pay influencers to hawk their products on YouTube or Instagram, Main Street One distributed its gun messaging to people on the internet with large social media reach. Using a database of nearly 10 million influencers on Instagram, Facebook, Twitter, YouTube, and Pinterest, it determined which Nevada “creators” were open to helping and had a certain reach among audiences of voters open to a public health message about guns: moms, first responders, health care professionals. Across the geographic footprint of Nevada, the company credentialed and recruited 287 influencers, many of them doctors and nurses, and told them to create their own version of a messaging brief, provided to them with a company dashboard.
[...] Whether that resulted in a lengthy blog post from a local activist or a Las Vegas–based influencer posting an Instagram selfie with an anti-gun caption, the campaign tracked which content performed best among persuadable voters, for 16 weeks until Election Day. It used traditional marketing KPIs—impressions, clicks, likes, earned-media value—but also machine learning to figure out which pieces of content were having the strongest impact on the online discourse. “I’d say 90 to 95% of the content we got off the bat is what we asked for,” said Ryan Davis, a senior strategist for Main Street One. “People are very clever these days.” By matching its analysis to the voter file with probability models, the team was able to watch which gun messages influence its target audiences. [...]
Hougland said the experiment was “privately funded,” and said some of the influencers, whether political activists or just fame-hungry Instagrammers, were compensated for their efforts. Others were given “social incentives”—badges, credentialing—instead of payment. “You can go to a big ad agency and pay 12 times as much, or you can go to citizens who agree with you on guns or women’s rights, but happen to make all their living by making content online by being a social influencer.
Darpa has financed a lot such discourse analysis research in academia etc. A possibly relevant recent paper under a Darpa grant "Detection of Promoted Social Media Campaigns"; see also "The DARPA Twitter Bot Challenge
". DARPA also has a fairly blurby page on a research program called "Social Media in Strategic Communication (SMISC)"
The general goal of the Social Media in Strategic Communication (SMISC) program is to develop a new science of social networks built on an emerging technology base. Through the program, DARPA seeks to develop tools to help identify misinformation or deception campaigns and counter them with truthful information, reducing adversaries' ability to manipulate events.
To accomplish this, SMISC will focus research on linguistic cues, patterns of information flow and detection of sentiment or opinion in information generated and spread through social media. Researchers will also attempt to track ideas and concepts to analyze patterns and cultural narratives. If successful, they should be able to model emergent communities and analyze narratives and their participants, as well as characterize generation of automated content, such as by bots, in social media and crowd sourcing.
At this point you're better off taking this to ai SE since Main Street One isn't disclosing specifics (and even getting details from DARPA is hard in terms of research output, rather than program goals) so you'd need/want some AI experts to guesstimate what Main Street One might be using (from the fairly large amount of academic projects that Darpa financed on this theme, some of which might have open-source output.)