The Google index is a database of all the pages on the web that the Googlebot has crawled. It stores textual information about webpages and all pages within the index have the potential to show up in the search results. Other search engines maintain their own indexes.
Given time your website should be indexed automatically. If you still feel it has not been indexed you can request Google to crawl an index your site within the Search Console by clicking "Fetch as Google" in the left hand menu. The index report, also in the left hand menu, will also show you how many of your pages are currently indexed.
The supplpemental index is a collection of secondary pages that Google deems to be less important and less trustworthy. Supplementary pages are far less likely to show up in the search results.