Cleaning linoleum floors is easy - by design. Most of these floors are "no-wax" (not an entirely accurate term) and come with a protective coating.
A caveat here: True linoleum - made of pressed fibers such as ground-up cork and wood dust - hasn't been manufactured in the United States since the late 1970s.
Sheet flooring today is usually made of vinyl, although people still refer to it as linoleum because this is what sheet flooring was called for nearly a century.
No-wax floors do shine without waxing, and the gloss layer will keep them looking good for a while. But with time and use, the layer will develop worn or dull areas that need to be coated wth a floor finish (wax!) to maintain its shine.
Cleaning linoleum floors weekly with a neutral pH cleaner - such as a little dishwashing detergent dissolved in lukewarm water - is the best way to keep that shine intact.
Other neutral best-bets for cleaning linoleum floors include a self-polishing, metal-interlock products (which contains zinc to bind the molecules for a stronger seal).
Non-neutral solutions can create a buildup over time that can damage the finish. Remember daily sweeping and damp mopping will help keep damaging dirt out of the house - away from your floor.
As part of your cleaning routine, you'll also want to:
Visit the Clean Organized Home Store for the linoleum floor cleaning products and tools you'll need to get started.