Dizer - It's when you say something to someone ( She said she was mad at Jhon - Ela disse que estava brava com o Jhon) ps: pay attention to the conjugation.
Simple Past - Eu digo, Você diz, Ela/ Ele diz, Nós dizemos, Eles / Elas - Dizem, Voces - Dizem
Falar - is the ability to talk either in your own language or in any other ( I speak English - Eu falo Inglês), you could also use it when describing the way someone talks ( She talks fast - Ela fala rápido )
Contar - To tell someone a story or a fact. ( She told me that he got fired - Ela me contou que ele foi demitido )
Hope this helps =)