Put on rubber gloves to protect your hands from the hydrogen peroxide.
Clean the crack with hydrogen peroxide and allow it to dry overnight.
Sand the crack with a 220 grit disc in the sander. For now, remove just the jagged edges that may be pointing up from the crack. You do not need to perfectly smooth out the surface of the vanity -- sanding it smooth will come later.
Place the color chart from the repair kit on the vanity and find the closest match. The repair kit comes with several tubes of material. Refer to the chart to find how much of each tube you need to mix together to get the correct match.
Mix the sealer, as indicated on the color chart, on a paper plate with a wood paint stirrer. Containers and paint stirrers made of other materials may alter the color of the crack sealer. Using a paper plate and wood stirrer will prevent any unintended color changes from occurring.
Apply with the paint stirrer just enough sealer to fill the crack, then smooth it out. Allow it to dry for several hours, according to the package directions, or overnight.
Sand excess sealer with a 220 grit disc, then wipe away the dust.
Sand again with a 300 grit disc and wipe away the dust. If needed, sand one more time with a 400 grit disc and wipe clean.