Summarize:

Are you hoping to change their mind about something? Is there someone else you're trying to protect? Perhaps you just want to feel more comfortable around them yourself. Before starting a conversation, make sure you know what your goals are in bringing up your concerns. It's possible that your goals can't be achieved. For example, you might wish that a much older relative would stop using a word you find offensive. However, they may be so stuck in their ways that having a conversation isn't going to yield your desired result. If your goal isn't achievable, choose one that is. You might not be able to stop your relative from using that word, but you can at least let them know how you feel about it. Choose a time and place when you can both feel comfortable. You should be able to have privacy and not feel rushed. You may want to let them choose the time and place. Let them know why you'd like to talk to them. You can say, "You said something the other day that I'd like to talk to you about. Are you up for that?" Let them know that you are assuming the best about them. You can say, "You said something earlier that I admit I found offensive. I'm sure you didn't intend that, but I'd like to talk about it." If the person is someone you know well and trust, keep that in mind. They may feel awful knowing that they offended you. If they're someone whom you don't know well or don't trust, keep that in mind, too. Consider whether the person has any motivation to change their behavior. For example, if their job is at stake, they will likely take this conversation seriously. If they're unlikely to ever see you again, they may simply brush off your concern. You can use your relationship to the person to help influence them. For example, you could say to a service provider, "I'd like to continue hiring you, but I feel really uncomfortable when I hear that kind of language." Or to a relative, such as your child, you could say, "I don't feel comfortable being around others when you speak that way." If the remark was particularly hurtful, tell the person that if it happens again, you will take action. This is generally appropriate when hateful words or slurs are used knowingly. In a work environment, you can say, "If I hear that word again, I'm going to have to speak to our supervisor." In a family context, you can say, "I think I will have to go home if you continue speaking like that." Just tell them straight forward. We usually overthink things and make the worst of it. Being straight forward does not mean that you should rub it in their face. You just have to say how you feel without gracing your self ego as well as theirs. People always try to tell some indirect stories and it ends up vindicating the other person. Knowing how you feel may help the person understand. They might not understand why what they said is offensive, but knowing that you feel hurt could be enough to help them change their behavior. Use "I" statements. This means saying, "I felt angry when you used that word to describe our coworker" instead of, "It was wrong of you to use that word to describe our coworker." Another example is saying, "I felt embarrassed when you told that joke" instead of, "That joke wasn't funny." Try to express your feelings without getting visibly upset. If the remark was extremely offensive, you may feel panicked or even start to cry. If this happens, that's okay. You may simply need to take some time and space before you can have a calm conversation. If you find yourself becoming upset during the conversation, excuse yourself. Say something along the lines of, "Please give me a minute, I'd like to discuss this with a level head."
Decide why this conversation is important to you. Ask the person to have a conversation. Remember who you're talking to. Prevent a second offense. Speak about your feelings.