If you have an old laminate floor that is solid and smooth, but you want a different look, you don't necessarily have to pull up the old laminate. Laminate isn't an ideal underlayment for most types of flooring, but if you go with a glueless vinyl floor, it should work just fine. Glueless vinyl floors come in square or rectangular panels that snap together along the sides to form the plane of the floor. Unlike traditional floating floors, they don't require an underlayment, and they can be cut with a standard utility knife.
Remove the floor trim throughout the room with a hammer and prybar. Remove it carefully, keeping it intact.
Set the first vinyl tile next to the wall at one end, with plastic shims between the wall and the tile to create a small gap there.
Clip the next onto the first one, next to the wall, again putting shims between the tile and the wall. Repeat and continue, snapping the tiles together all along the wall to form the first course.
Cut the last tile in the course to fit against the far corner, using your razor knife to score the surface alongside a square and then bending the tile until it breaks.
Set the second course in place alongside the first. If you're using a kit with square tiles, then line the up in a grid pattern. If the tiles are elongated planks, then stagger the ends between courses. Cut the ends as needed.
Work your way across the whole floor, course by course. Cut the final course so that it fits against the ending wall with about 3/8 inch of space there.
Reinstall your floor trim using your hammer and trim nails. The trim will cover the gaps by the walls.