Help me write an Apex test class (future apex class)

I have written an apex trigger which calls a future method. The trigger method passes a list of accounts that are serialized and does some processing. The trigger/class works great. My problem is, I dont know how to write the test class for it. I am getting 0% coverage on the handler class. I am also getting a System.JSONException: Malformed JSON: Expected '[' at the beginning of List/Set Error. I need someone to help me write this test class with proper coverage. I have posted the question on stack too (link below) so if someone can answer it there then it would be great. I prefer NOT to give access to my org/sandbox so if we need to meet to code, we can. Would like a day turn around because its just a test class.

https://stackoverflow.com/questions/68120928/salesforce-test-class-getting-system-jsonexception-malformed-json-expected

https://developer.salesforce.com/forums/ForumsMain?id=9062I000000DMEEQA4