When Did Blacks Get To Vote In The U.s.?

In the legal context, the black people got the right to vote after the Civil war in 1865 by the fourteenth and the fifteenth amendment. The fifteenth amendment states that '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 race,
color, or previous condition of servitude.'
However, many people share the view that although the constitution now recognized the right of blacks to vote, it was not for may years that they were actually able to. Many states passed laws that impeded their voting in one way or the other. There was a literacy act where only literate people were allowed to vote. Since most of the black people were illiterate back then, a majority of them could not vote. Also, some states required voters to pay a fee/tax to register for voting. This automatically excluded the poor people. Most black people lived in poverty at that time and hence, this too indirectly took away their right to vote. Many other similar gambits were employed that disallowed black people to vote.
The true change, and hence the true right to vote for the blacks cam after the Civil Rights movement in 1960. At this time, segregation between the black and the white was finished off formally (such as combining black and white schools). One important name to take here would be of Martin Luther King, Jr. Who worked hard in ensuring that the blacks got their right to vote and other privileges that are due for every citizen.

Maybe it was 1961or 62?

The black people legally got the right to vote after the Civil War in 1865 according to the 14th and 15th amendment of the constitution. The article 1 of the 15th amendment says: "The right of citizens of the United States to vote shall not be denied or abridged by the United States or any State on account of race, color, or previous condition of servitude."
However, there has been much talk about whether this was the time when they actually got the right to vote and not just on the legal paper as they say. States passed laws that did not deny the black people to vote but rather made it impossible for them to do so. For instance, there was a literacy law that stated that only literate people who could read and right could vote. Most of the black people were illiterate back then and this really impeded their right to vote. Other gambits that were used included paying a tax to vote (obviously the poor and the blacks-who were mostly poor were excluded in this way).
In its true sense, blacks got the right to vote after the Civil Rights Movement in 1960's. Black and white separation was bridged and schools merged for both. The black people were recognized and were empowered to render the impeding laws of voting null.
One name that is very important in helping the black people to truly be able to vote and stand up for their rights is Martin Luther King, Jr.