You have to make sure that the quote tags stay intact. Sometimes one of the brackets will get deleted if you are deleting part of the post.
Another way to quote is to copy/paste the text, highlight it, and then click the quote icon which is the white bubble thing all the way to the right of all the icons above the text box. If you want it to say the persons name then you have to do it like in alasdairms post, writing out the equal sign followed by the name, after the word 'quote' in the first tag.
You shouldn't have to go through all the trouble though, and clicking the quote icon on the bottom right of a persons post should work just fine.