To get your website showing up in search engines (such as Google etc.), you need to submit it to be indexed/crawled. Indexing/crawling is when a search engine examines all pages within your website, and adds your content/references to your content to their database.
When a user searches for something on Google your website will show up in their search results if your content matches their query.
To get this set up you first need to sign into/create your Google account. Sign into Google and then navigate to Google Search Console
Select 'Start Now', and then choose the URL prefix option. Enter your website's address including the full protocol (https:// etc.).
Continue to the next step for domain verification
Select the HTML Tag verification method
Copy the HTML code that's been generated for your website
Before verifying with Google, you need to open the content management system for your website and save the verification code.
Navigate to Website Settings > General Settings > Search Engine Optimisation and paste the code into the field labelled 'Google Search Console Verification Text'
Save these changes, then Publish to your live website. Waite a minute or two for your live website to rebuild, then you can go back to Search Console Tools and verify your domain.
Once your domain has been verified, within the Search Console Tools navigate to 'Sitemaps'. Your website automatically generates its own sitemap, so at the 'Add new sitemap' section you just need to type in 'sitemap.xml'.
The sitemap contains all pages/links within your website, so Google now has all of the information it needs.