I've noticed that many people are nervous and worried about having conversations about race. But I have some tips that will help you moving forward.
Be Talkative: Have conversations about inequity and harmful racially based behavior BEFORE an event happens. You can hopefully avoid the negativity and defensiveness of REACTING to harmful behavior.
Be Quiet: When a Black person is sharing a personal story about oppression, resist the natural urge to relate in that moment. No matter how closely your story relates, if you are not Black it does not relate.
*An actual hack* the phrase "Thank you for sharing..." can be used in about 90% of interactions and will be appreciated by the speaker.
Don't worry about offending Black people. Your new racial awareness does not need to be discussed with the Black people in your life. In fact, if you're doing the work properly you should be having fewer conversations with Black people. Listen when a Black person speaks and then converse about positive change with the white people in your life.