Women in the United States gained the right to vote with the ratification of the 19th Amendment to the U.S. Constitution on August 18, 1920. This amendment legally guaranteed American women the right to vote. The struggle for this right took decades of activism, starting notably with the Seneca Falls Convention in 1848 and including various tactics such as petitioning, protesting, and lobbying. While the 19th Amendment granted voting rights nationwide, some women of color still faced discriminatory barriers for years afterward. The amendment's text states, "The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex".
In other countries, the timeline differs, for example, in the UK, some women gained the right to vote in 1918, but equal voting rights with men were achieved later in 1928.
If you want information about women's voting rights in a specific country other than the US, please let me know.