Single plugin fix

1. Install ‘WP No Category Base‘ WordPress plugin. You will not require to configure any settings.

Dual plugin fix

1. Install and activate ‘Redirection‘ wordpress plugin

2. Install and activate ‘Decategorizer‘ wordpress plugin

3. Go to Tools -> Redirection and type ‘category’ in ‘Source URL’ textfield and save it

After installing one of the above options your new url will be
http://www.mysite.com/blog/
instead
http://www.mysite.com/category/blog/