Open the System Preferences. This can be done by either clicking on the System Preferences icon in the Dock or by going to Apple Menu > System Preferences.
Open the Security & Privacy pane by clicking Security & Privacy.
Make sure that the General tab is selected. Click the icon labeled Click the lock to make changes.
Enter your username and password into the prompt that appears and click Unlock.
Under the section labeled Allow applications downloaded from:, select Anywhere. On the prompt that appears, click Allow From Anywhere.
Exit System Preferences by clicking the red button in the upper left of the window. You should now be able to install applications downloaded from the internet.
While holding down the control key on your keyboard, click the application's icon once to make a dropdown menu appear.
Select Open from the menu. A new window will appear.
Click Open in that window to launch the application. You should only need to do this once per application, on the first launch. After that, you'll be able to launch the application any way you like.