When someone add you to be a member of a blog ,an email will be sent to inform you about the invition ,if you have an account then go to your account and look at the upper center of Blog manager page , as you can see :



After you clicked on invition link , you will promoted to next page ,select the invition you want to accept or decline , and click on the accept or decline buttons :

 

When you accept the invition , you will be directed to Blogs manager page , and you can start posting to that blog by clicking on the Member in link :