What follows is my attempt to make some sense of those idea. To begin with, I found this definition, from the "What in the hell..." blog, useful in figuring out what some of the stakes are in Negri:
Marx defined real subsumption of labor in the “Results of the Immediate Process of Production,” the so-called unpublished sixth chapter of Capital Volume One (a translation here). Real subsumption is defined in contrast to formal subsumption of labor. Formal subsumption occurs when capitalists take command of labor processes that originate outside of or prior to the capital relation via the imposition of the wage. In real subsumption the labor process is internally reorganized to meet the dictates of capital. An example of these processes would be weaving by hand which comes to be labor performed for a wage (formal subsumption) and which then comes to be performed via machine (real subsumption). Real subsumption in this sense is a process or technique that occurs at different points throughout the history of capitalism. For some thinkers, such as Antonio Negri, real subsumption of labor is transfigured into real subsumption of society such that all of society becomes a moment of capitalist production. In this version of real subsumption is an epoch, a stage of capitalism within a historical periodization, analogous to postmodernity.
"Real subsumption" is akin, then, to post-Fordism or the "social factory"; the move from formal to real subsumption is arguably a matter of technological development, as directed by capitalism. Technology reorganizes society to lend support to the imposition of wage labor, and the commoditization of more and more of everyday life, of "living labor" or even life itself, as a presupposition, a given. So those of us who precede the "digital natives," for instance, are subject to "formal" subsumption of friendship -- suddenly being "paid" a kind of wage for translating their social lives into preformatted data. Digital natives will be subject to "real" subsumption, in that using social media, etc., will seem like the necessary precondition for friendship.
I don't know how useful that jargon is, ultimately, but it captures an important "passage," as Negri would say, in the conjoined development of technology and capitalism. Capitalism continues to expand as it must by subsuming more of social life to the way it organizes relations, configuring encounters as opportunities for commodification and profit extraction, as moments of competition between exchanging parties -- as moments of class struggle, in Negri's account.
The point of emphasizing the passage from formal to real subsumption is to highlight it as a point around which resistance can be organized. In general, if you accept that our being or subjectivity is economically determined, then the function of dialectical criticism is to open up imaginative spaces in which resistance to determinism can be conceived -- cracking open the surface of relations to reveal hidden "contradictions" as moments of possibility, of alternatives, of autonomy and opportunity for self-determination.
A critique of technology can be organized around preventing the formal-to-real-subsumption passage, preventing the implementation of technology to grease the skids of this epochal transformation. One way is the "Luddite" approach of rejecting technology, breaking machines, clinging to outmoded work processes that may limit productivity gains but also prevent deskilling from being implemented by management through technology. Or to expand that to Web 2.0 conditions, one rejects social media to prevent social deskilling, the erosion of social skills. We refuse to let convenience and efficiency govern social lives, avoid the seductive trap of narcissism that technology lays out for us, and instead choose slow, more difficult social relations characterized by less frequent but more intensive face-to-face communications. The point is to resist the mediation of sociality, resist turning our various intimate communications into moments for capitalistic commodification, even when they promise to enhance our personal brand or bring us profit/attention/social recognition (on capitalism's terms). But this strategy has the disadvantage of forcing those who adopt it to live separately from the mainstream of society, as conscientious rejectors, which ultimately isolates them and makes them an ignorable subculture within a capitalist society that proceeds without them.
One can alternatively proselytize for dropping out. One could try to use subversively the technology that capitalist development has brought, deploying it against the real subsumption it is designed to foster. In other words, one could use social-media technology to continually announce the dangers incipient within it.
That seems somewhat facile (the subsumption captures resistance; it makes Che into Che T-shirts) and open to accusations of hypocrisy (though it is basically what I do -- I'm doubling down on hypocrisy here), which is probably why Negri and his followers advocate pushing through this passage, totalizing it, and seizing that complete unification of the working class in social life as always already production as the condition of the transition to communism. But such a program still seems like cooperating with capital, merely relabeling its prerogatives with radical terminology. At this point I am content to try and think about how formal and real subsumption are progressing on the front of everyday life. The relevant terminology for that seems to be things like affective labor, immaterial labor, emotional labor, erotic capital. One way of understanding neoliberalism, too, is to see it as the passage to real subsumption.
Anyway. Even when I can't figure out what Negri is getting at in his glosses in Marx Beyond Marx, he consistently excerpts fascinating passages from the Grundrisse. I think this is pretty awesome, for example:
Capital's ceaseless striving towards the general form of wealth drives labour beyond the limits of its natural paltriness [Naturbedürftigkeit], and thus creates the material elements for the development of the rich individuality which is as all-sided in its production as in its consumption, and whose labour also therefore appears no longer as labour, but as the full development of activity itself, in which natural necessity in its direct form has disappeared; because a historically created need has taken the place of the natural one. This is why capital is productive; i.e. an essential relation for the development of the social productive forces. It ceases to exist as such only where the development of these productive forces themselves encounters its barrier in capital itself.
This strikes me as a key idea about technology with respect to capital. Pursuit of profit (i.e. the elaboration of the capital relation) drives us to extend our ideas of what is "necessary" in life -- beyond the classic Conan formulation of "Crush your enemies, see them driven before you and hear the lamentations of the women," if you will. So cooperation with capital appears to be an extension of the self, McLuhan style -- an opportunity to become more "all-sided" and thus consume/enjoy more, and regard these acts of consumption as fundamental to who are. That is, we start to regard consumption as "productive," as expressing our basic capacity to do things. Marx seems to suggest here that "individuality" as we experience it is actually contingent on capitalism -- the degree to which we are constituted by the relations it posits. This is why "individualism" should be held in some suspicion -- this seems easier to do, actually, with the advent of technology, as this kind of individualism now so obviously manifests as personal branding. (Maybe there is some sort of negation of the negation at work. Individualism that was once a product of "real subsumption" suddenly seems an alien thing that we are obliged to operate, develop.)
It seems to me that we then come to depend on the technology, as it is embedded in capitalism, that elaborates consumption as opportunities for self-expression. Mediating consumption makes it appear productive: To the consumers, it makes it expressive of the self to an audience as opposed to a private moment of sustenance, and to capital, mediation makes consumption into data that is raw material for further production (i.e. it becomes more capital). We cooperate willingly with the subsumption process because it appears as a kind of liberation into a new of wonderful all-sidedness, even though these new sides are opened to us only as moments of exploitation, ultimately -- the new sides are just new ways to work for someone else through the technology. But the hope is that we can reclaim these new sides to ourselves and render them autonomous from capital. That seems to be Negri's hope anyway, and the healthy gist of the argument in Multitude as I understand it.