It's pretty easy.
Click on the Design tab, then click Edit HTML. Search for the </head> tag.
Paste this in the line after </script> but before </head>
<script src='http://apis.google.com/js.plusone.js' type='text/javascript'/>
Save your template and you are ready to go. You will now have a Google +1 button at the bottom of every post.
UPDATE! Apparently, you can also update and add the +1 button by clicking on the Design tab, then clicking EDIT in the Blog Posts box, uncheck and re-add the "Show Share Buttons" and it will be there as well.