So - first, go into the post you are wanting to edit, or start a brand spankin' new blog post if you're feeling so inclined. Write to your heart's content :)
When you've finished writing your post, you are going to select (with your cursor) the text that you want to set apart. Once you have that text highlighted, you're going to click the quote button. It'll look like this:
That's it. Really, it's that easy! Sometimes doing this can add a strange space either before or after the blockquote, so make sure you preview your post to make sure it looks the way you want.
After you've done all that, you should have a pretty blockquote that will look something like this :)