How were women eventually granted the right to vote?

Fighting for it through multiple years, 1919 the 19th amendment was passed and women could then legally vote.

The 19th amendment passed by Congress allowed all the women in the country the right to vote.

Explanation:

The 19th amendment was passed on June 4, 1919 by the Congress and was officially came into existence on August 18, 1920. From 19th century many women protested, participated in civil disobedience, wrote and even lectured about it. Some suffragist suffered in prison by voting illegally. They believed that this will bring a great change in their constitution. In United Kingdom some women achieved it in 1881 but achieved national hood only after 1907. After decades of sufferings Saudi Arabia has granted the rights to vote only in 2011.