When creating or editing a post in Blogger in the WYSIWYG "Compose" box, you can simply paste html code for a video and it will appear embedded.
Beginning in YouTube,
Click the "Share" button below the video you would like to embed.
Then click the "Embed" button.
An html code will appear in the dialogue box.
You may need to resize the video for it to fit in the Blogger frame. The 560x345 pixels size should fit.
Now, copy the embed code and simply paste it where you would like it to appear in your blog post! It will appear as code at first, but once you post, it will appear as the embedded video.
Here is a Blogger "Help" video on embedding YouTube.
