What is the best way to baby proof our stairs?

Baby gate. Invest in a good baby gate to avoid the infant from falling down the steps.
Block them. Toddler gaits on each end. Make sure the uprights are close enough so the child's head and body cannot fall through. If they are too wide, cover with netting.
Gates are easy. Putting up a gate at the top and the bottom of the stairs will prevent your baby from either falling down or climbing up (and then falling down!).