The Apps Script snippet will insert an image at the current cursor position of the Google Document. You can either specify a web image (url starting with http), or if the image file is in your Google Drive, you can specify the full file URL (right-click a file in Drive and choose Get Link).

function insertImage() {
  // Insert a web image
  var image = 'http://img.labnol.org/logo.png';
  var blob = UrlFetchApp.fetch(image).getBlob();

  // Insert an image from Google Drive
  var image = 'https://drive.google.com/open?id=xyz';
  var fileID = image.match(/[\w\_\-]{25,}/).toString();
  var blob = DriveApp.getFileById(fileID).getBlob();

  var doc = DocumentApp.getActiveDocument();
  var cursor = doc.getCursor();

  if (cursor) {
    cursor.insertInlineImage(blob);
  } else {
    doc.getBody().insertImage(0, image);
  }
}