Following Options can be used to debug Lightning Aura Component JavaScript Controller.

Option 1:

console.log() statements can be used.

Option 2:

Breakpoints in the Browser.

Sample Lightning Aura Component:

Component:

<aura:component implements="flexipage:availableForAllPageTypes" access="global" >
    <aura:attribute name="testingVar" type="String"/>
    <aura:handler name="init" value="{!this}" action="{!c.init}"/>
    <lightning:card>
        Sample Lightning Component
    </lightning:card>
</aura:component>

JavaScript Controller:

({
    
     init : function( component, event, helper ) {
        
        component.set( "v.testingVar", "Sample" );
        component.set( "v.testingVar", "Example" );
        let tempStr = 'Testing';
        
    }
    
})