Sand the quartz surface with a hand-held sander, using the 200-grit sandpaper pad. Use smooth, even strokes and make sure to sand the entire surface. As you work, you may need to wipe away dust with rags. Repeat this process using increasingly finer grit sandpaper pads, ending with the 800-grit paper.
Clean the quartz countertops with a damp rag followed by a dry rag to remove all excess particles created by sanding. Buff the countertops with a polishing pad and stone polish. Be sure to choose a stone polish for use with quartz and follow the instructions on the product's label. The quartz surface should now be nice and smooth.
Tape off your counters with masking tape and any other adjacent surfaces which are not quartz. Then, seal your countertops with a stone sealant approved for use with quartz. Follow the instructions on the sealant's label. Some sealants are sprays while others require you to brush them on with a paint brush. Allow the sealant to dry for the recommended time on the sealant's label, usually between 24 and 36 hours.