Easiest way to get this is by buying 50 bronze packs which cost you 400 coins each. 400 X 50 = 20,000 coins. There are some ways though to get it easier.
-If you've got the ultimate edition you will be able to open a pack every week for 24 weeks.
-You can open 4 packs on the FUT web app which can be found on http://www.ea.com/uk/football/login?redirectUrl=http://www.e...
but I'm not sure if they count. Thanks to Trueachievement for pointing out you get 4 packs in the game itself OR you can open the 4 packs in the link.
- Besides if you complete 12 challenges like change your ball, stadium, shirt and open a pack you will get a gold pack for free as well.
-By downloading the Web app and logging in onto the web app you get a mini pack free. (thanks to LEboueur for confirming this counts)
-There are some cups and tournaments in ultimate team which reward you with a pack if you win the tournament. Rewards for winning each tournament can be found in the description of the tournament.