If you want a user to be able to edit a blog, you have 2 choices, either create a new role and add the user to the role and then grant the role edit permission on the page containing the blog or edit roles on the blog, or you can also assign a specific single user edit permission.
Click the gear icon next to the title of the blog to get to feature instance settigns, then on the security tab you can see where you can enter a user or assign a role.
Hope it helps,
Joe