Sample Code:

//Pass dependent field parameter e.g.: Account.YourDependentField__c
public static Map<Object,List<String>> getDependentPicklistValues(Schema.sObjectField dependentField){
        Map<Object,List<String>> dependentPicklistValues = new Map<Object,List<String>>();
		//Get dependent field result
        Schema.DescribeFieldResult dependentFieldResult = dependentField.getDescribe();
		//Get dependent field controlling field 
        Schema.sObjectField controllerField = dependentFieldResult.getController();
		//Check controlling field is not null
        if(controllerField == null){
            return null;
        } 
		//Get controlling field result
        Schema.DescribeFieldResult controllerFieldResult = controllerField.getDescribe();
		//Get controlling field picklist values if controlling field is not a checkbox
        List<Schema.PicklistEntry> controllerValues = (controllerFieldResult.getType() == Schema.DisplayType.Boolean ? null : controllerFieldResult.getPicklistValues());
        
		//It is used to decode the characters of the validFor fields. 
        String base64map = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/';
        
        for (Schema.PicklistEntry entry : dependentFieldResult.getPicklistValues()){
            if (entry.isActive()){
			//The PicklistEntry is serialized and deserialized using the Apex JSON class and it will check to have a 'validFor' field
                List<String> base64chars = String.valueOf(((Map<String,Object>)JSON.deserializeUntyped(JSON.serialize(entry))).get('validFor')).split('');
                for (Integer i = 0; i < controllerValues.size(); i++){
                    Object controllerValue = (controllerValues == null ? (Object) (i == 1) : (Object) (controllerValues[i].isActive() ? controllerValues[i].getLabel() : null));
                    Integer bitIndex = i / 6;
                    Integer bitShift = 5 - Math.mod(i, 6 );
                    if(controllerValue == null || (base64map.indexOf(base64chars[bitIndex]) & (1 << bitShift)) == 0){
                        continue;
                    } 
                    if (!dependentPicklistValues.containsKey(controllerValue)){
                        dependentPicklistValues.put(controllerValue, new List<String>());
                    }
                    dependentPicklistValues.get(controllerValue).add(entry.getLabel());
                }
            }
        }
        return dependentPicklistValues;
    }