Simply click on the icon that looks like the one displayed above.
Upon opening, the store front page will look similar to this:
From here, simply hover the mouse over an app and an Add to Chrome option will appear. Click on that option to install automatically. Alternatively, to find out all about an app before installation - click on the app image. Something like the image below will appear where you can find out everything you need and click the Add to Chrome option to install:
Once installed, the application will appear automatically on the applications list as part of the Chrome home page.