Okay, I finally got it all figured out. Just for the benefit of any poor sucker like me who is super confused at first by testing, all you are trying to do is programtically reproduce user actions. So in my case, the user clicking a button sends the case number associated with a pete item into my trigger. I needed to programatically recreate that so my function could be tested. In this case, it requires creating a test account, contact, case, and pete item, all linked together. Then I just pass my pete item (that only exists in temporary space) into my actual script that I care about. Below is the working code, I really hope it helps somebody so they don't have to go through the same crap I did. Notice how at the end, the test function calls the main functions with the same type of data being passed that the function would normally expect from a user interaction.

public class AutoFillPete
{
    public static void PETEFILL(PETE_Items__c[] pete)
    {
        for (PETE_Items__c p:pete)
        {
            CASE[] contactResult = [SELECT ContactId,AccountId FROM CASE WHERE id = :p.Case__c];
            ACCOUNT[] accountResult = [SELECT CID__c FROM ACCOUNT WHERE id = :contactResult[0].AccountId];
           
                 if(contactResult.size() > 0)
              {       
                p.Contact__c = contactResult[0].ContactId;
                p.Account__c = contactResult[0].AccountId;
                p.CID__c = accountResult[0].CID__c;
              }
        }
    }
   
    public static testMethod void PETEFILLTEST()
    {

            //Create an account and retreive account #
            Account AccountMake = new Account(Name='test123'); insert AccountMake;   
            ACCOUNT[] getAccountId = [SELECT Id FROM Account WHERE name = 'test123'];
           
            //Create a contact that belongs to the account we just made, and retreive the ID
            Contact ContactMake = new Contact(LastName='testJohnson', AccountId=getAccountId[0].Id); insert ContactMake;
            CONTACT[] getContactId = [SELECT Id FROM Contact WHERE LastName = 'testJohnson'];
           
            //Create a case that belongs to the contact we just made, then fetch it's ID.
            Case CaseMake = new Case(ContactId=getContactId[0].Id, Status='open', Problem__c='Other', Origin='Phone', Subject='testcase21313213', description='test case of joy', PETE_ID__c='ADY2342342' ); insert CaseMake;
            CASE[] getCaseId = [SELECT Id FROM Case WHERE Subject = 'testcase21313213'];
           
            //Create a PETE item, and link it to the case. Then pull it's ID.
            PETE_Items__c PeteMake = new PETE_Items__c(Name='TestItem', Description__c='This is a test', Case__c=getCaseId[0].Id, Present_in_Build__c='2526 (Taxport)', How_to_Reproduce__c='Eat Magic', PETE_ID__c='ADY2342342'); insert PeteMake;           
            PETE_Items__c[] getPeteId = [SELECT Id, Name, Case__c FROM PETE_Items__c WHERE Name = 'TestItem'];

            //Call the main script that autofills those boxes, and pass the array returned from the above query.
             AutoFillPete.PETEFILL(getPETEId);

    }
}