The settings for Live Search can be found in the Search Element, and in the Global Options at Options > Search > Search Form tab. If you turn it on, you will see many options underneath it to control its appearance and functionality. You can set a minimal Character count for it to kick in, limit the number of posts the live search will suggest, control the height of the Live Search Results Container, and control whether the featured image and post type are displayed in the results.
Results show as soon as the minimum number of characters is reached (see image below). However, if the user hits Enter after they type, the search page will load instead.