Here is a passage from USCIS website concerning your question.
Who is Eligible to Apply?
"Asylum may be granted to people who are arriving in or already physically present in the United States. To apply for asylum in the United States, you may ask for asylum at a port-of-entry (airport, seaport, or border crossing), or file Form I-589, Application for Asylum and for Withholding of Removal, at the appropriate Service Center within one year of your arrival in the United States. You may apply for asylum regardless of your immigration status, whether you are in the United States legally or illegally."
So, determine your local USCIS office, file form I-589, and gather all your possible documents. (this should be a starting place for you.!)
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