While both linoleum and vinyl are relatively easy to install as compared to other flooring types vinyl does have a bit of an edge because it offers several installation options.
Linoleum over vinyl flooring.
Check for protrusions such as nails and pound them back into place.
Work backwards out of the room to let the tiles dry.
Clean and repair the floor.
Over the top ceramic and stone tile vinyl and laminate flooring tile and sheet linoleum hardwood planks and decorative concrete can all be installed over existing linoleum.
Clean the vinyl floor thoroughly with tsp to remove dirt soap and oil residue.
If any parts of the vinyl or linoleum flooring have begun to bulge up slice out the bulge with as utility knife.
If the old floor has a rough texture or some indentations use a coat of embossing leveler.
Vinyl has the advantage for diversity of design and low cost while linoleum will wear longer and is a much more natural less toxic material.
Spread vinyl tile adhesive over the old linoleum with a trowel and press the tiles into place in the pattern and layout you determined earlier.
Both vinyl and linoleum flooring have merits as relatively low cost flooring materials where an easy to clean clean water resistant surface is desired.
Linoleum or vinyl flooring.