How did the twelfth amendment change the electoral process?

It provided that the Electors should vote separately for President and Vice President. Previously the VP had been the runner-up in the Presidential election (each elector having two votes). In 1796 this resulted in a Federalist President (Adams) having a Democratic-Republican VP (Jefferson). In 1800, determination to avoid this led to a tie between the DR Presidential candidate (Jefferson) and VP candidate (Aaron Burr); hence the change.