The world of fashion is one of the best places to search for signs of millennial spirit. If you look at what designers are creating for 2000, you'll find an overall atmosphere where everything is over the top, pushed to the outer edges and carried to astonishing extremes, from which there are several prevailing themes: futuristic, fantastic high-tech; the return to nature/bohemian/ethnic roots; eclecticism, bricolage and the patchwork crazy-quilt layering of diverse styles and influences; plain weirdness.
A simple explanation for all this is that we're behaving this way because we feel poised to enter "the future" ready for a lifestyle change; that at the same time we're nostalgically clinging to he past and want to relive it as it slips from our clutches (or that, indeed, we wish to return to it and deny futurism); that we're summing up our history by piecing bits of it together in a hodgepodge I-want-it-all manner; that we want to be vividly different in honor of the new millennium, and the only route open is weirdness.
To put together your own millennial look via the medium of makeup and hair, I advise a playful approach to the whole thing. Get creative, and put together your own interpretation that incorporates some or all of the above.