Steps on how to add Addthis button to your every post:
1. Goto Blogger. Go under Design tab. Click on Add a Gadget.
3. Goto Addthis Website and Signin to your account. Select how you want your Addthis button to display. Now generate an addthis button for Blogger.
4. Copy that code and paste it on your new Gadget Window.
5. Save Gadget. Make sure gadget is placed below Blogpost. To show it after every post.
Sample of this is below this post.