The answer to 'best way to clean grout' is to use a grout brush and a grout cleaning solution. Start by sweeping or vacuuming the grout to remove any loose dirt or debris. Then, mix a grout cleaning solution according to the manufacturer's instructions and apply it to the grout. Use the grout brush to scrub the solution into the grout, working in small sections. Rinse the area with clean water and repeat the process if necessary. For heavily soiled grout, you may need to let the cleaning solution sit for a few minutes before scrubbing.
Proper grout cleaning can help maintain the appearance and longevity of your tile surfaces. If the grout is severely damaged or discolored, you may need to consider grout repair or replacement, which is best handled by a professional cleaning service.