To remove old vinyl, remove the transition strips (Image 1) that hold the carpet in place.
Use a heavy-duty scraper to remove the old vinyl (Image 2). It is hard work. The old vinyl will probably come up in small pieces and in some areas the paper backing separates from the vinyl itself and remains on the floor.
Tip: If you have a large amount of vinyl flooring to remove, you might consider renting a power scraper. They are available from most rental outlets and you can rent them by the hour.
With the old vinyl removed, the only way to remove the remaining paper backing and dried glue is to use an adhesive remover. Apply it with a brush and spread it out evenly. This glue is extremely strong, so use a fan to ventilate the room to the outside of the house. Once the glue soaks it, the paper backing and vinyl come up much easier.
If there is a notch left in the carpet where the bar was, cut the carpet back to create a new straight line.
Once the floor is clean and thoroughly dry, set the new vinyl in place. Make sure it is straight and then use a straight edge to trim it along the walls (Image 1).
At the carpet, trim the vinyl back to fit just underneath the edge.
Once the vinyl is trimmed and in position, roll half the vinyl back and begin applying the adhesive. Use a trowel with 1/8” teeth and spread the adhesive (Image 2) evenly. It is important to cover all the floor with adhesive — do not leave any bare spots. Because it is concrete, you can apply the vinyl after the adhesive is on the floor. Roll half the vinyl onto the adhesive.