https://support.google.com/blogger/answer/42673?rd=1

Control permissions

Watch a video about permissions and privacy

By default, your blog is completely public, and can be read by anyone on the internet. However, if you want to keep it private, just click on "Edit" under the Blog Readers section in the Settings tab. 

Under the Blog Readers heading, you'll probably see "Anybody" selected as the default. When you change this to "Only these readers," you'll get an option to add readers.

Click the Add Readers link and then enter the email address of a person to whom you want to grant access to your blog. To add multiple people, separate their addresses with commas.

For each address entered, the Google Account associated with that address will be given access to view your blog. If an address is not associated with an account, that person will be sent an invitation email with a link allowing them do one of three things:

• Sign in to an existing account
• Create a new account
• View your blog as a guest (no account required)

In the first two cases, the reader will be given permission to view your blog whenever they are signed in to their Google Account. As a guest, they'll be able to continue viewing your blog through the link in the invitation email, but this will expire after 30 days. After that, they'll need a new invitation.

If you want to revoke someone's access to your blog, simply click the X link next to his or her name in the Blog Readerslist. You can also go back to the "Anybody" option any time you decide to make the blog completely public again.