Normally, you would get an invitation email, requesting you to join this blog page. The email would look like this:
One has to click on the link and keep following the directions, which should be routine. However, there is one place I have seen where there might be a bit of confusion. Suppose you are visiting the page http://noncommutativegeometry.blogspot.com and you are not logged into google in any other browser tab or window. Then the screen will have a link "sign in" on the top right. You click on it and keep following the directions, you will soon reach the following screen:
Merely typing your google username here does not work. You have to type your username with "@gmail.com" appended at the end.
To avoid all this unnecessary hassle or lengthy procedure at various points, best thing is to create a gmail account (which you can do now by going to the page http://www.gmail.com), log in to gmail and then open another browser tab and visit this page.