Putting vinyl down might be a whole nother deal. everything is not a pretty as one might think under carpet.
The carpet will be stapled in place and you just have to start pulling up the corners, if you can grab it with a pair of pliers. If not cut a slot so you can get a crow bar under it to get it started.
Each step and riser is often a separate piece. Then you pull off the underlay and then you have mountains of staples to get out. Only then you can stand back and see what needs to be done for the next layer of flooring.