Hi Ravi,

Thanks for your response!  You assumed correctly.  The button is on Programming and the User List is a related list.  They are linked by Lookup fields...they are not Master/Detail.

I'm still a little stuck...here's what I have so far....

I added the recordID attribute to my component:

<aura:component controller="User_List" implements="flexipage:availableForAllPageTypes">  
    <!--aura init handler , call js "loadUserList" function on component load, and display contact data on table-->   
    <aura:handler name="init" value="{!this}" action="{!c.loadUserList}"/> 
    
    <!--Declare Attribute for store User Records List-->  
    <aura:attribute name="ListOfUsers" type="User_List__c[]"/> 
    <aura:attribute name="recordId" type="String" />

  <div >   
    <button class="slds-button slds-button--brand slds-button_stretch" onclick="{!c.downloadCsv}">Export User List</button> <br/><br/>

    </div>
</aura:component>

I then added the compenent.get to my controller: 

({
    // ## function call on component load  
    loadUserList: function(component, event, helper){
       helper.onLoad(component, event);
    },
    
    // ## function call on Click on the "Download As CSV" Button. 
    downloadCsv : function(component,event,helper){
        
        var programmingID = component.get("v.recordId");
        
        // get the Records [User_List__c] list from 'ListOfUsers' attribute 
        var stockData = component.get("v.ListOfUsers");
        
        // call the helper function which "return" the CSV data as a String   
        var csv = helper.convertArrayOfObjectsToCSV(component,stockData);   
         if (csv == null){return;} 
        
        // ####--code for create a temp. <a> html tag [link tag] for download the CSV file--####     
	     var hiddenElement = document.createElement('a');
          hiddenElement.href = 'data:text/csv;charset=utf-8,' + encodeURI(csv);
          hiddenElement.target = '_self'; // 
          hiddenElement.download = 'User_List.csv';  // CSV file Name* you can change it.[only name not .csv] 
          document.body.appendChild(hiddenElement); // Required for FireFox browser
    	  hiddenElement.click(); // using click() js function to download csv file
        }, 
 })

Do I need to add anything to my helper? Like should I also be adding "component.set" for the programming?
 

({
    onLoad: function(component, event) {
        //call apex class method
        var action = component.get('c.fetchList');
        action.setCallback(this, function(response){
            //store state of response
            var state = response.getState();
            if (state === "SUCCESS") {
                //set response value in ListOfUsers attribute on component.
                component.set('v.ListOfUsers', response.getReturnValue());

            }
        });
        $A.enqueueAction(action);
    },

Finally, I'm not sure how to phrase my WHERE statement in my class.  I thought I would say WHERE the lookup fields matches my variable, but I get errors so I'm assuming I misunderstand.  
 

public class User_List {
 
@AuraEnabled
   public static list <User_List__c> fetchList(){
      
      List <User_List__c> returnUserList = new List < User_List__c > ();
        
      for(User_List__c ul: [SELECT 	id, First_Name__c, Last_Name__c, Email__c, Extension_Number__c, Type_of_User_License__c, Phone_Model__c, Language__c, Outbound_Number_Display__c, Outbound_Name_Display__c, Voicemail_Option__c, CFNR_Number__c 
                            From User_List__c 
                            WHERE ul.Programming__c = programmingID
                            LIMIT 1000]) {
             returnUserList.add(ul);
          }
         return returnUserList;
   }
}

Any additional help would be appreciated!!