I watched a video on YouTube and it was a romance video in how to romance Jacob in Mass Effect 2. The female Shepard has a black and gold long dress on. I would like to know how to get it. Do you need a DLC or do you just find it randomly?
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 videoshows 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).
To swap casual outfits, go into an armor modification station on the Normandy. On the left side of the screen will be two tabs, one for armor, one for casual appearance. Select the casual appearance tab and cycle through your options.
This video shows someone going through a lot of casual outfits after doing some modding to get more, but it shows exactly how to swap casual outfits.