I did several times keep getting the following statement:

"You don't have access to this property. Verify this property or ask a property owner to add you as a user."

I have followed the video you are showing me. Several times.

Am I missing something on website showing I am the owner? Is this the Admin area?

Are you logged into your WordPress as an Administrator when you try to do this?

Which part are you having difficulties with?

I go to google.com/webmasters/
Click add property
Put in my website address http://name of website
use recommended methods
Copy the tag (which is the whole thing "try between quote marks but does whole thing "
Go back to my dashboard..click into all in one SEo
go down to general setting to webmasters verification
then to webmaster tools and put copy of tag from google
erase everything before and after "keep info between"
go down and click update
go back to google page and click verify
just did again and showed failed

Did you remove the quote marks? It's important to only use the bit after the first quote and before the second quote.

When you verify are you telling Google which method you're using?