At this month's Sydney Drupal meet up I did a presentation about Search in Drupal 8. In the video, I explain three ways you can create a search page, they are as follows.

1. Core Search

The core Search module which comes with Drupal has some new functionality in Drupal 8. The biggest change is the ability to create custom search pages without using any other module.

2. Views Filter

A common way to build search pages in Drupal 7 was to create a views page and use the "Search Keywords" filter in views. This can still be done in Drupal 8 and best of all Views is now part of core.

3. Search API

The Search API module is used to create powerful search pages and it's highly extensible. It is the module to learn and use for building search pages.