They did this by bringing in Conservatives and Segregationists via the "Southern Strategy" after the 1969 Presidential election. By bringing in the Wallace voters (15%) into the Republican Party, plus the white voters that voted for Nixon (45%) you get the white majority. To do this, you need to purge the Republican party of liberals and minorities.
Reagan's "Welfare Queens who drive Cadillac's", "War on Drugs", "Tough on Crime", "Willie Horton" ads, "People on Welfare are lazy", these slogans have the subliminal message of equating "Crime with being Black" "Poor blacks with laziness". It plays on suburban white fears and stereotypes to divide conservative white suburbans against minorities and offend moderates and white liberals.