Strange Coins are used to buy Exotic pieces of armour from Xur. The main way to get them is by completing Weekly Heroic Events. Only level 22 and 26 version of the weekly heroic event will reward 3 Strange coins for completion, and 28 will reward 6 Strange Coins. You can complete all these level per week to get a total of 12 Strange Coins. On the other hand these strange coins can also be found in the rare engram and gold chests. Now the question is where and how you can find the Xur, Agent of the Nine, because you cant see him every time.

How To Find Xur, Agent of the Nine

If the game datebase is correct then Xur only appears between: Friday 9:00 AM PST to Sunday 9:00 AM PST

So basically only over the weekend. You can buy one exotic armor piece per class and exotic weapon and exotic engram.

How to Get Strange Coins Guide