Best way to include featured image in search results?

Hello, When I do a category search, the results are displayed with featured image. But a search through the search bar does not include the featured image. What is the best way to include the image in the search results? Thank you! And bonus question - I'd prefer the search and category results have the image float to the left of the title, meta info, and excerpt (excerpt is currently blank). Is there a good way to do this? Thanks again!