How can I change casual clothing in Mass Effect 2?
The specific clothing option you're looking for is called 'Evening Wear' - it is only available as part of the Kasumi - Stolen Memories DLC. You can customise your armour and casual wear by using the armour locker aboard the Normandy SR-2 which is available on the CIC deck next to Jacob and (I believe) in the captain's quarters.
Once you have activated the armour locker screen, select "Casual Appearance";
If the dress was longer than this (http://jamiecotc.com/ME/femshep/headache.jpg) then the person who made the video altered their game files to use other assets, like the dresses the asari wear. In order to do that, you'll need to edit your coalesced.ini file. This video
shows the various outfits that unlocks for both Broshep and Femshep, and has handy links in the description.If the dress was short, though, you just need to buy and play Kasumi: Stealing Memory (and then enjoy what happens when you go talk to Garrus about something other than calibrations).