Test post, using Blogger Insert Video toolbar button.
Go to YouTube.
RH click in browser address bar and Copy link to video.
Back to Blogger.
Choose Insert a Video button.
In dialogue box select YouTube and then Paste video address from step above.
A list of video thumbnails will appear.
Choose the one you want.
Video is inserted.
Publish Post button.
Done as seen below.
Same video posted in another way:
Got to YouTube.
Below viewer, look for Embed tab and click it.
Accept defaults, but choose Custom size - type 500 into width box. RH click and copy code.
In Blogger in New Post tab.
Type Title, etc.
Click Edit HTML tab.
Scroll to end of all visible text and Paste code.
Check it out - Note selecting too large of a video size in YouTube may affect how the blog is shown, i.e. it should not be wider than other postings and thus encroach on RH menus or push menus to bottom of blog - hence the 500 width.