There are many examples of Jim Crow laws that mandated segregation in various aspects of life in the time period you are asking about. Please follow the links below for many more examples than I can give in this space.
One famous example would be the rules about where blacks could sit on busses in Montgomery, Alabama. There, blacks and whites could not sit in the same row of seats. Whites filled the bus from the front and blacks from the back. When the bus filled up, blacks would have to stand up and give up their seats if any further white riders boarded the bus.
Another example has to do with waiting rooms in bus stations (for long-haul busses like Greyhound). Southern states had laws that said that whites and blacks had to have separate waiting rooms in the stations. They also had to use separate restrooms. This sort of law was what the Freedom Riders were fighting against.
Finally, there was a great deal of segregation in education. At the K-12 level, there were black schools and white schools and black students could only attend black schools even if they lived near to the white schools. This sort of thing is what the case of Brown v. Board of Education was about. There was even segregation in higher education. For example, up until James Meredith entered the school under federal protection, no African American student had been allowed to attend the University of Mississippi.
There were, of course, many other laws. These covered such things as drinking fountains, swimming pools, and libraries. Please follow the links below for many such examples.
The legacy of Jim Crow laws extends from 1874 through later end of repeals in 1975. The idea behind the laws was to create a two-tier society in the South. Ideally the reason was to increase white masculinity while decreasing Afro-American masculinity. The reasoning was reparation for the humiliation of the South by Union forces. It did not help that during reconstruction there was blanket amnesty to all whites in the south who participated in the Civil War. This put ex-confederates back into seats of power wiping away all the advancement of African Americans politically. The term Jim Crow comes from the series of laws that were in part to 1) disenfranchise African Americans and 2) reinstate White superiority. Laws like, the poll tax, the grandfather clause, marriage licenses, interracial dating, and vagrancy were used to strip African Americans of their protections that the 13th, 14th and 15th Amendments gave them. The Plessy v Ferguson(1896) court case made segregation legal in the south. De-segregation was slow, after World War II, President Truman ended segregation in the United States military. It took Brown v. Board of Education (1953) to end segregation in schools and ultimately the Civil Rights Act of 1965 to end racial discrimination.
To continue with what pohnpei397 stated about some examples of segregation, Jim Crow, and higher education is that at the higher education level African-Americans who wanted to take college courses had to sit in the annex of a classroom during lectures. It was also a law that African-Americans were not allowed to enroll or be admitted into higher education on the grounds that the schools did not support integrated education. The two examples that I have provided took place in Oklahoma and Texas four years prior to Brown vs. Board of Education.
Jim Crow laws impacted all parts of life for African-Americans from transportation, health, and education. In Virginia, African-Americans had to sit in certain seats to attend any place of entertainment such as an opera house, theater, or public hall.