Are you talking about yourself or trying to convince some else? My impulse is to give rational explanations or credible evidence. If someone doesn't believe that the world is round, and the proof is something you cannot see with your own eyes, I would say we need to have faith in the people who tell us the world is round. Teachers and scientists are people who proved their reliability by helping society in ways that we can see on a daily basis, so we should trust them when they say the world is round because we have faith in their competence and honesty.

Self worth is also something you cannot really see with your own eyes. So, likewise, you need to have faith in the opinions of people who have earned your trust. Such people could include therapists, teachers, friends, and anyone you know to be honest and intelligent.

Sometimes, you can trust the evidence of your own experience and knowledge. My family often tried to convince me I was worthless and stupid. I would say they were wrong because I got good grades so I was obviously not stupid. Worth is a little harder to define than intellect, but I used my family's determination to control me to mean I had some value they wanted to exploit.

If you have doubts about your worth, consider if there has been someone who wants to stay in your life whether or not you want them to. Usually, such a person will try to convince you that you are worthless because they are afraid of losing you. Also consider what abilities and personality traits you have that people want or benefit from. Worth can be defined more materially as having a positive impact on society either by doing good or doing no harm.

If you are talking about convincing someone else of something they refuse to believe, you might have to accept that you cannot change their thinking. Sometimes, insecurities make people afraid to look at a truth that is looming over them. Sometimes they simply do not have the mental ability to understand something that you know.

I hope that helps.