Here is another great tutorial: https://www.designertrapped.com/how-to-paint-your-linoleum-floors-yes/
This is Linda. Here's an article with several ideas about painting a design on a vinyl/linoleum floor. Click on the link for each project for directions. Of course, you don't have to actually paint a design. You can paint it a solid color. In that case, check out any of the paint designs for the basics. Preparation is the key to success here and it's best to use a paint designed for floors. Other than that, it's a process. Sand, clean, prime, paint, seal. That may sound like a lot of steps, but if you want the floor to last longer it's the best way to go. It's also a good idea to give the floor an extra coat of sealer every year or so. That helps protect it even longer. Wishing you the best.
Here is how I did it at my niece's house: https://thehoneycombhome.com/how-to-paint-linoleum-flooring/
Here you go! https://www.viewalongtheway.com/2013/01/how-to-paint-vinyl-or-laminate-flooring/?crlt.pid=camp.admnF6qtputu