To seek asylum in the United States, you need to show that returning to your home country would mean facing persecution or that you have already been subjected to persecution for valid reasons.
According to Cornell Law School, valid reasons to seek asylum include that you would face persecution for your activities in a social group, religion, nationality, race or political opinion.
When you prove that you previously faced persecution in your home country, you have a valid reason to expect future issues. This will qualify you for asylum under the law. There may be exceptions if there have been significant changes in your country due to a change of leadership or political changes, so keep that in mind.
No past persecution
If you have no history of persecution in your country, you have the burden of proof. You must show valid evidence that there is no doubt you would have trouble if you return.
You will have to show conditions that exist in all parts of the country because the U.S. authorities can determine you would be safe in a different part of your country. You also need to show there is a reason behind your fear, such as the persecution of others in your same situation.
U.S. authorities can grant you asylum even if you do not fully prove your case, but this is highly up to their discretion. You should not bank on getting an exception.
Seeking asylum does not mean you will automatically get it. You will need to prove your case well enough to meet U.S. regulations.