You can either buy Coins on the market, in the trading area of the forum or with real money.
For more information on how to buy Coins, you can click on the P in the sun above your farm.
In order to activate your premium account, click on the aforementioned symbol, and then on "Exchange Coins".
You'll see a selection box in which you can choose one, six or twelve months of premium.
After the activation, your premium account is all set, and you can see the duration of your premium account on the bar below the symbol.