This is a hard question to answer since it depends on the basis of your claim. It's very individual.
Generally speaking, you want to provide evidence that you yourself are under threat or have been personally attacked or that your life is specifically in danger. Strong supporting evidence would be things such as police reports of attacks against you or hospitalization records in the event you were hurt. If there are communications (such as emails) specifically threatening you or newspaper articles where you are mentioned (e.g. if you are a political figure or if an attack on you is mentioned), this is good. People typically also includes information to support the claim that shows evidence of general persecution or general conditions in the country where you are living (e.g. evidence that a group of individuals or religion or political group you are part of is persecuted in the country where you are living). However it's quite important to have evidence that shows you yourself are facing this situation through the type of evidence I mentioned at the beginning.
At some point there will also be an evaluation of IFA (internal flight alternative). IFA requires you to prove there is nowhere in your current country you can relocate to in order to be safe. It means that you have to prove that you will continue to be in danger no matter where you live in your country.
I'm sure others will have more to add.