Offer to install it to people who experience difficulties with Windows, and never lie about it being much simpler or N times faster; don't forget to ask first if they use any special software/hardware that requires Windows or has only Windows drivers. Offer alternatives, but always be clear that they're not the same thing. 99.9% of non professional Office users wouldn't even notice the differences with LibreOffice, but that's not a good reason to tell them that the two products are identical: they're not, but one is open and free, both in price and in how it respect the user, which for many people could count a lot more than the extra features MS Office has over LibreOffice.
One thing that worked for me many times is that I always offered full support for any problems the user would encounter, and to install Windows back and for free if after a given period of time they didn't find Linux usable for them. One has to understand that the common non tech user trying Linux can't easily phone their friends, coworkers, kids, nephews, etc. not even the PC repair shop down the street and magically find a Linux expert, so they must be given something that works and is well supported.
Word of mouth will do the rest: most users don't care about pervasive advertising or spyware, Closed vs Open Source etc, but others do, and they're the ones telling about Linux and bringing other users in.
My comments not really about whether it works, as we know it does, it's about how we go about getting the word out there.