The key to installing tile over a formerly carpeted area is to remove as much of the adhesive as possible. Typically, carpet installers install carpet padding with thin, easily removed zigzag adhesive lines. Use a common floor scraper to scrape away the glue. Floor scrapers are made for removing drywall mud, mortar, paint and other materials; the tool perfectly suits adhesive removal. Target the thick, zigzag adhesive lines, doing your best to pry under the adhesive with the scraper's blade. Scrape the adhesive until you expose the gritty concrete surface beneath.
Chemical Adhesive Removers
Don't use a chemical stripper to remove the adhesive. Thin-set mortar manufacturers explicitly note avoiding chemical adhesive removers, which contain chemicals that melt carpet adhesive, causing it to permeate deep into the concrete's surface. In worst-case scenarios, this may prevent a tile bond and keep you from being able to tile the floor at all.
Testing for a Good Bond
Thin-set mortar manufacturers recommend checking a concrete substrate's permeability by applying water to it. Sprinkle water on a test area. If it soaks in, chances are the substrate is ready for tile because adhesive can bond. If the water beads up and sits on the concrete, wipe it away and scrape some more. Repeat the water test until the entire floor (or stubborn adhesive areas) accepts water. Allow time for the floor to dry before installing tile.
Use special flex-blend polymer-modified thin-set mortar for tiling over preexisting carpet. Don't use a non-latex, basic thin-set mortar. Spread an anti-crack membrane over any visible substrates cracks. Before proceeding, make sure the installation surface area is free of dust and sediment. As carpet removal is a dusty job, wear a particulate dust mask and ventilate the work area.