If you can separate yourself from the household member during their 10-day isolation period, you do not need to quarantine unless symptoms develop. We recommend getting tested 3-5 days after your last contact with the household member, and to mask in indoor public spaces for 14 days.
If you are unable to separate yourself from the household member, or if you have ongoing contact with them (like a child or family member that cannot care for themselves), you do not need to quarantine unless you develop symptoms. Try to minimize contact and consider masking around them, if reasonable. We also recommend masking in indoor public spaces for 14 days. Get tested 3-5 days after their positive test, and again 3-5 days after they completed their 10-day isolation.
Whether you're separated from them or not, if you develop any symptoms of COVID-19, get tested and isolate, pending results.