After you have successfully uploaded a video to Youtube.com, then below the video click SHARE > EMBED to get the embed code. The code will look something like this (you don't need to understand the code in order to use it):
<iframe width="560" height="315" src="https://www.youtube.com/embed/HEVBWRzU5SA" frameborder="0" allowfullscreen></iframe>
Then if you want to embed the video into a blog post, then click the orange pencil icon to open the post editor. Note that you have to be in the HTML mode. Note also the width of the video above is 560px and this may be wider than your blog post column width. To change, click the SHOW MORE below, select CUSTOM SIZE
Click in width field and type a number suitable for your blog post column width then click in the HEIGHT field. The height will automatically be added such that the aspect ration is maintain so video wouldn't be distorted.
If you want to embed the video in the sidebar, go to Dashboard > Layout > Add a gadget > Add a HTML/Javascript gadget, paste the code into the field and save. Note: if you don't know the sidebar width, go to
Dashboard > Layout > Template Designer > Adjust width
and you can see the sidebar width there (also total width - sidebar width = blog post column width)