This article explains how to submit your website to Google (search engine indexing). This will add your website to Google's inventory and allow it to be delivered as a result in searches by other Internet users.
You already have a Google account.
Adding Your Website to Google
Through the Google Search Console (formerly Google Webmaster Tools), you can add your website to Google's index for free. This allows your website to be displayed as a result in Google searches. The article Google Search Console: Confirming Domain Property Ownership takes you step-by-step through the submission process.
You can also find out how to create a Google Sitemap in the article Creating a Google Sitemap.