How do I change my ugly linoleum flooring?

Does the flooring you want to put down float, or is it the type requiring adhesive? You're in a catch 22 if the old vinyl is from the early 80's and back, as there is a likelihood of asbestos contamination if you scrape it up. If there's any question on the age of the old floor, and you have to glue down the new, you may want to consider nailing down a lauan underlayment, or something similar.

floating floor can just sit right on top no?

It sure can, Terri. There is a thin pad that you will be stapling down to the old floor, the new floating floor will rest on that.

You can put it right over the surface as long as it's clean and flat. You can use a surface leveler that's similar to patching plaster you use to fill holes in walls. It's a light and will fill in seams or dents. You can keep it a thin layer so it only fills in the imperfections. The thing to prepare for is how the new flooring will meet up with other surfaces. It looks like your floor abuts carpeting. That might be an issue if your new surface is much higher than the carpet. I would avoid adding anything that will add to your flooring thickness. Then look to see how you will treat the new edge. Of course clearance under doors may need adjusting but that's fairly easy.

When we had new flooring put in our older home they checked to make sure there wasn't other layers of lino under the one we were covering. It becomes an issue if there are multiple layers. I don't recall why, besides weight, but it's something to look into. You might want to pull up a corner in your closet just to check.