You can lay vinyl or linoleum over old linoleum if the old floor is in good condition. If it is loose or has large holes in it, you are probably better off removing it. Fill minor holes with wood glue and spread a coat of embossing leveler over the floor to smooth a rough surface or fill in small dents. Allow the leveler to dry for at least 24 hours before installing a new floor.
If you decide to remove the linoleum instead, proceed with caution. Though true linoleum is a green product without harmful chemicals, asbestos tiles were commonly used in the early to mid-20th century. Do not remove asbestos tiles, but leave them in place to avoid asbestos contamination. The adhesives used to install linoleum may also contain asbestos. When in doubt, contact a professional. To remove linoleum, pull it back and discard it. Rent a steamer from a home improvement store and steam the floor to soften adhesive and tar backing. Scrape it off and discard it.
Once you've made repairs to the old linoleum floor or removed it, you're ready to install the new floor. Linoleum tiles are simple to install yourself, but installing sheets of linoleum is tricky because the flooring shrinks slightly when exposed to adhesives. Hire a contractor to install it instead for best results. Wait at least 24 hours before moving furniture in place or walking on linoleum.
Vinyl floors are often referred to as linoleum, even by retailers and distributors, but the two products are very different. Vinyl is a synthetic product made from chemicals. It has a pattern is printed on the top layer. Vinyl is susceptible to damage from knives or impact. Linoleum is a completely natural product, made from linseed oil, cork dust, wood flour, tree resins, ground limestone and dyes. It is very durable and comes in a variety of brilliant colors. When buying flooring, use the two terms correctly to get the flooring you want.