A floor that's real linoleum requires different cleaning methods from flooring made of vinyl. Avoid strong soaps and detergents; alkaline cleaners deteriorate and crack the surface over time. The best cleaners are pH-neutral, but when you need a little more cutting power for streaks and grime, turn to those bastions of household versatility: vinegar, baking soda and the safest cleaner of all -- water.
Unlike vinyl flooring, linoleum is an all-natural product made from pine resin, wood chips and linseed oil, and it has a finish much like that of a wood tabletop. Strong solvents and harsh detergents can damage it, and linoleum manufacturers typically recommend cleaning only with the pH-neutral products that they sell. The main ingredient in one such product is dipropylene glycol methyl ether, which is a mildly oxidizing cleaner. If you don't have access to these products, you can wash linoleum with a mixture of cleaners you already have around the house.
Clear water is the mildest cleaner you can use on your linoleum floor, but even that requires care, because allowing water to stand on linoleum can stain it. To increase the dirt-cutting power of pure water, add an ounce of dish detergent per gallon of cold water. Use this solution by loading a microfiber mop, wringing it thoroughly and mopping a 5-by-5-foot section. Rinse the mop in a separate bucket containing clear, hot water, again wringing the mop thoroughly before mopping. Finish cleaning that section of the floor by wiping it dry with a clean rag.
Vinegar is an effective cleaner and disinfectant, but it's acidic and can dull a linoleum finish, so it's best to use it in moderation. Adding a quarter cup to 2 gallons of warm water to which you've already added an ounce of dish detergent should be safe, though, especially if you wring your mop, clean the floor in sections, rinse and dry. Include a quarter cup of baking soda to this mixture to help cut grime and deodorize. If you don't like the smell of vinegar and don't want to wait for the odor to dissipate -- which doesn't take long -- add a dash of your favorite essential oil for fragrance.
Make an alternative vinegar cleaner for your linoleum floors that cuts grime quickly and is especially effective for use as a pre-wash for polishing by mixing equal parts of vinegar, rubbing alcohol and water. Rubbing alcohol is a solvent that can dissolve wax, polish and even some types of dye stains. The stronger vinegar concentration may dull the finish, which is why you should use this cleaner only before polishing. Adding a drop or two of essential oil makes this cleaner more pleasant to use; choose pepperminty oil if you want to repel ants and mice.