The health certificate should go to the health and epidemic prevention station, Haidian District Health and Epidemic Prevention Station (in Beijing Seismological Bureau). If you live near the West Fifth Ring Road in Haidian District, you can go to Shijingshan Health and Epidemic Prevention Station (behind Shijingshan Hospital). Cost 108 yuan.
A temporary residence permit requires your ID card, 3 photos and a rental contract. Just take all the documents to the police station in your area. It only takes a few minutes. 5 yuan. However, it is usually handled by the landlord. You can ask the landlord if he can help you.