Here's how to go about doing it. On your browser, go to www.blogger.com, and you will be brought to your own account page - (draft.blogger.com) - remember to log-in first. This is where you will see your subscribed blogs listed. See picture.
To post on any of the listed blog, click the "Pencil" icon adjacent to the blog title. You will then see the usual New Post page. Good luck. :D
This is how I would do since there is no "New Post" button on the menu on the home page yet.
|Click on the icon circled in red to post new|