Look, there's my Mii! I've earned 280 Platinum coins already, and I can do missions to earn more!
Check it out, and start earning those coins!
(UPDATE) I forgot to click on a bunch of the completed missions, so now I'm at 440 Platinum coins. Things like linking your facebook, twitter and google+ accounts to My Nintendo, gets you points very easily. Gold coins come from purchasing games, and the blue Miitomo coins come from activities done in Miitomo, obviously.