To enable the search results filtering by product attributes values first you have to set the search filter attributes. In order to do it please go to Products > Settings > Product Attributes, find the product attributes that you want to make a search filter from and check the Search Filter checkbox near it.
As soon as you check the checkbox near the attribute it will become a search filter.
Show search filter drop downs near the search box
You can show the search filters near the search box or not. In order to show the search filters please check the Show Attribute Filters checkbox in the Product Search wiget on Appearance > Widgets screen.
When you check the Show Attribute Filters checkbox and save the widget all the Search Filter attributes drop downs will show up near the search field.