Before you decide to install a linoleum or vinyl floor over an existing floor you need to find out the recommendation from the manufacture of the new floor.
Some floors are not ridged enough to be installed over a flooring that may give in to dents from furniture or appliances. As a rule I feel it is better to remove the existing flooring when possible, especially in areas of heavy traffic such as kitchens and other main living spaces.
However at times it does make sense to prepare the existing floor for installation over a old floor. This could be in a bathroom with little traffic or on a wood subfloor where the removal of the flooring would cause damage to the underlayment adding another unwanted expense.
In the case of a overlay, the floor must be clean or stripped and if any embossing (uneven surface design) is in the floor it will need to be coated level with an embossing leveler or floor patch designed to bond to the old floor. I like to use a sanding block with 100 grit paper or courser to scratch up the surface of the old floor before coating, to create a better bond.
Once the floor is coated, smooth and dry, sometimes taking two to three coats depending on the floor and your skill; the floor is ready for a normal installation.
It is a good idea to let the adhesive flash off a bit longer than normal so as not to trap too much moisture between the two floors. The moisture in the glue will not have the opportunity to absorb into a wood or concrete subfloor since the vinyl floor is above and below the adhesive.
Be sure to use proper pads and castors on all furniture since you now have a floor that has double the coushion and may dent easier.