Choose your Almama and Alpapa (Alpacas who are at rest will not appear in the list). Make sure to check the breeding fee. If the breeding fee is more than 10 ALPA, it means this Alpaca has already bred before. More babies an Alpaca has made, more breeding fee they require.
After you have chosen the Almama and Alpapa, click "Bang Bang". (If it's your first time playing with the breeding feature, there will appear a pop-up window from MetaMask for you to approve the contract).
After the transaction is done, you can see your egg in "Alpacas" page. Every new eggs requires 5 minutes' wait before it is ready to hatch. Click "Hatch" and, after you pay the gas fee, your fresh Alpaca will appear in the "Alpacas" page.