First, you will need to sign up for Google Recaptcha (https://www.google.com/recaptcha/).
Select Recaptcha V2. Add the necessary domains your site will be accessed by into the fields provided.
Take note (or keep the browser tab open) of both the Site Key and the Secret Key. You will need these for the next step.
Login to Umbraco CMS > Go to the Content section > Expand Website Configuration > Click on Global Settings > Scroll to Form Settings > Paste your Site Key and Secret Key into the respective fields provided.
The pre-built Contact Form and Newsletter Form supplied with your Umbraco theme from uSkinned will now work with Google Recaptcha validation.
Bonus Step (Umbraco Forms)
If you plan on using Umbraco Forms then you will need to take this additional step to successfully set up Google Recaptcha for any Umbraco Form you create.
Open your website in a code editor such as Visual Studio Code. Locate the file ~/App_Plugins/UmbracoForms/UmbracoForms.config:
<setting key="RecaptchaPublicKey" value="sHZZenninFziVUV9TN24FqhwZvc2b4e8BLrG" />
<setting key="RecaptchaPrivateKey" value="sHZZenninFziVUV9TN24FqhwZvc2b4e8BLrG-" />
Enter the site keys you have already created and update the code above.