First, do you really need to? You may be able to lay new floor over top. To remove heat with a blow dryer for a couple of minutes then remove tile with a putty knife. Sand away extra adhesive.

Wear safety glasses to protect your eyes from flying debris when scraping off the old vinyl tiles.
Use a heavy-duty metal scraper to work under a tile and begin prying the tile free. It is usually easiest to start with an edge tile or a tile that is already loose.
Heat the tiles with a hair dryer or heat gun to soften the adhesive if you find it difficult to remove the tiles.
Continue using the scraper to remove the vinyl tiles until all tiles are removed.
Use a commercial floor adhesive remover to remove any adhesive residue from the floor. Follow all instructions carefully and wear any recommended safety gear.
Clean the floor to prepare for the new flooring.