How can I easily replace carpet with vinyl flooring?

There are some beautiful peel and stick vinyl options that would be easy and manageable for you. Some look like tile and some wood. Lowe’s or Home Depot will be willing to teach you how to DIY.

I do not know how big your area is but either square or rectangular vinyl peel and stick tiles or vinyl wood look planks (floating floor) are fairly easy to apply once you have the carpet pulled up and the floor cleaned up. And they are very reasonable in price, wear well, and clean up nicely. You will be up and down on your hands and knees and it gets a little hard on your back--so take your time or enlist the help of some younger relatives or friends. If your area is big--you might consider some sheet vinyl rather than individual tiles. Sometimes Home Depot will install for a very minimum price depending on how much you buy.

Your biggest problem is NOT putting down new flooring. It is removing the carpet. You will be down on your knees. Make sure you have a way to more easily get up when you need to.

You can generally start pulling up the carpet in a corner. Grab the carpet corner with a sturdy pair of pliers and pull up and then back toward you. Most wall-to-wall carpet has a tack strip along the wall next to the baseboard. This tack strip will provide most of the resistance. However, it is possible your carpet could be glued down. If this is the case, the job will involve a lot more prying and tugging. In any case cutting the carpet into smaller sections will make it easier to deal with. It there are tack strips remove them. If there is glue residue the job just became much more difficult, because you have to remove as much of the glue as possible before you can put down any other flooring.

Carpet glue residue is most often removed by first applying boiling water over an area and letting that sit for 3 to 5 minutes to soften the glue, then using a floor scraper: https://www.betontools.com.au/image/catalog/Marco%20Pesaro/FS150.jpg A less dangerous method is to use a chemical adhesive remover to soften the glue. A low VOC type is recommended, but good ventilation should still be provided. Here is one, though I have not used it: https://www.homedepot.com/p/Klean-Strip-Green-1-gal-Floor-Adhesive-Remover-GKGF75015/206804537?MERCH=REC-_-PIPHorizontal2_rr-_-100271088-_-206804537-_-N If you are in good physical shape you may be able to do the above removal in one or two days. However, be aware of your limitations. It's better for the job to take longer than for you to injure yourself. As to installing new flooring, there are a lot of videos online to explain how both pros and DIYers did a job. Do a search for "installing vinyl flooring video".