Your blog editor must have the HTML tab on the post editor if you want to insert YouTube videos into your post. Typepad, Blogspot and many others have this HTML just beside the Rich Text or Compose Tab.
Inserting YouTube Videos on your Blog
Go to YouTube Video that you wish to insert in your blog. You will see a Embed Box beside your video.
Copy the text in it and paste in the HTML of your post editor. Do not paste in the Rich text or Compose of the post editor. After that you may click on your Rich Text or Compose tab of the post editor. You should see the YouTube Videos appearing on it.
I have pasted the Embed Code and the YouTube Videos now appear below.