There are several ways to reply on the new board, and each way has a slightly different way to quote. The first and most obvious, is by clicking the button present at both the top and bottom of the thread. This will bring up a reply window with the last page of the thread at the bottom in a section called "Topic review." If you'd like to quote any of the posts in the thread, simply scroll until you find them, highlight the text you want to quote, then click the "Quote" button on the right hand side (shown in the image below).

That will grab only the text you've highlighted and pull it into your reply as a quote. You can continue to scroll through and quote other posts, so it's possible to answer to several members/posts in a single reply. Of course if you aren't replying to anyone in particular and are just sharing your thoughts in the thread, you won't need the quote.

The next reply method is by scrolling down to the bottom of the thread, where you will see a reply box. This is called the "Quick Reply" because it allows you to add a quick response without clicking the reply button. It's nice, because it's fast, but it isn't fully featured like the Reply button is (hence the name quick). There are no smilies and no attachment boxes to allow you to upload pictures. If you need those, just hit the reply button. To quote messages using the Quick Reply simply scroll up, highlight the text you want to quote, the click the "Quote" link on the left hand side under the member' name and online status (see image below)

Again, you can do this for as many posts as you'd like to quote.

The last method is to click this button in the bottom right of any message you want to quote. This will grab the entire contents of the message and open a reply window with them in it. Please go through and delete any non-relevant portions, usually you don't need to repeat someone's entire message, and your message may get lost in the shuffle if people are reading through a giant quote to find out what you have to say.