Put on rubber gloves to avoid skin irritation from the adhesive remover.
Apply adhesive remover with a paintbrush to the stuck-on adhesive glue from the self-stick laminate tiles. Allow the adhesive remover to sit on the glue and soften it as directed by the manufacturer's instructions.
Insert the edge of a scraper under the softened glue. Scrape the glue off of the floor to remove it. Repeat this step to remove all the adhesive from the laminate flooring.
Fill a bucket with undiluted white vinegar. Soak a scrub brush in the vinegar and tap the excess liquid back into the bucket.
Scrub the floor to remove any last traces of self-stick adhesive residue. Rinse the brush as needed. Wet the brush with more vinegar and continue to wash the floor.
Dry the floor with clean cloths. Allow the flooring to air-dry completely before installing the new flooring materials.