On your profile page, click on the headline of the blog post you would like to edit. You are now looking at the full post, and can edit it by clicking on the "Edit" link in the lower right hand corner.
When you are done, click on the "Update" button.
The "Delete" button erases the entire blog post.
The "Cancel" button erases just your current edits and revert the post back to the way it was before you started editing.