Practicing mindfulness while completing a daily activity is ultimately about making that activity your focal point. As you grow a formal mindfulness practice through meditation, breathing exercises, or other movement based practices, you can bring the mindset you have cultivated into other activities.
Brushing your teeth is a great time to practice as there are lots of sensations to notice and for those with electronic timed toothbrushes, the practice duration is timed for you so no need to worry about loosing track of time. Making brushing your teeth a time to practice mindfulness can also help you bring awareness to the quality of your brushing and reduce multi-tasking (no phone scrolling when you're practicing!).
How to Practice Mindfully Brushing Your Teeth
Notice sensations in your body - your feet on the ground, your clothes on your skin, the feeling of your inhale and exhale.
Notice the feeling of your toothbrush in your hand - it's texture, weight, etc.
Notice the your toothpaste - does it have a particular texture or smell?
As you brush your teeth, bring awareness to the sensations exactly as they are in this moment. Notice if your mind wanders, release the thought or feeling, and invite your awareness back to your brushing. Remember that releasing your thoughts or feelings is a practice - it's going to happen!