On iPad:
If you can't drag and drop the objects in a code-building program/website, such as the App Lab on code.org, make sure AssistiveTouch is turned off. To turn off AssistiveTouch, go to Settings>Accessibility>Touch and toggle off Assistive Touch, then reload the web page.
For App Lab, the drag-and-drop works best from the trackpad and not the screen. You might also need to long-press an object before it becomes dragable.
If the drag-and-drop still doesn't work, try loading the page in a different web browser.