package wstestclient;

import org.w3c.dom.Document;
import org.w3c.dom.Element;
import org.w3c.dom.Node;
import org.w3c.dom.NodeList;
import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.DocumentBuilderFactory;
import java.io.File;
 
public class WsTestClient {
    public static void main(String[] args)
    {
        try
        {
            File xmlFile = new File("D:\\WebApp\\NewServlet.xml");
            DocumentBuilderFactory documentBuilderFactory = DocumentBuilderFactory.newInstance();
            DocumentBuilder documentBuilder = documentBuilderFactory.newDocumentBuilder();
            Document document = documentBuilder.parse(xmlFile);
            document.getDocumentElement().normalize();
 
            NodeList nodeList = document.getElementsByTagName(document.getDocumentElement().getChildNodes().item(1).getNodeName());
            for(int tmp = 0; tmp < nodeList.getLength(); tmp++)
            {
                Node node = nodeList.item(tmp);
                if(node.getNodeType() == Node.ELEMENT_NODE)
                {
                    Element element = (Element)node;
                    System.out.println(element.getElementsByTagName("author").item(0).getChildNodes().item(0).getNodeValue()); //ошибка здесь
                }
            }
        }
        catch (Exception e)
        {
            System.out.println(e.getLocalizedMessage());
            e.printStackTrace();
        }
    }
}

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<blogs>
  <author>Pavel</author>
  <language>Java</language>
</blogs>

NodeList authors = element.getElementsByTagName("author")
Node firstAuthor = authors.item(0);
NodeList firstAuthorChildren = firstAuthor.getChildNodes(); //здесь возникает ошибка java.lang.NullPointerException
Node firstAuthorChild = firstAuthorChildren.item(0); 
String  value = firstAuthorChild.getNodeValue();