Who is the woman on the US 1 dollar coin?

If you mean a dollar minted in 1935 or earlier, it's Miss Liberty, as in "Statue of ..."

If your coin is dated 1979-81 or 1999, it's a picture of woman's rights activist Susan B. Anthony.

If it's golden in color and dated 2000 or later, it's the Native American guide Sacagawea who helped the Lewis and Clark expedition.