In admin under Settings > Permalinks, select Custom Structure and enter /blog/%postname%/.
This will prepend /blog/ to categories and tags by default, and any custom post types and taxonomies where you have not registered them with the with_front argument set to false. you can remove it from the built-in category and tag taxonomies by setting category base and tag base (also under Settings > Permalinks) to category and tag, respectively (or whatever you want your bases to be). The end result will be that only posts will contain the blog prefix.