How do I get my image into first place?

Image captions are considered in image ranking. The better the image description matches the user's query, the more likely it is that the image is shown on the first page of search results.

The quality of the site where the image is placed, as well as the quality of the image itself, also affect ranking. For more information on what makes a high-quality site, go to Tips for webmasters in the Yandex.Webmaster Help.

Each image in the search results has a link to the page whose description of the image best corresponds to the user's query.

Note. Yandex finds images that best match the user's query. However, image captions aren't the only ranking factor, so the words from the query may be missing from the pages that contain the images.

The site is in the search results, but its images are not

It's likely you're comparing Yandex search results with image search results. However, Yandex.Search and Yandex.Images use different ranking algorithms. For your website images appear in search results, make sure they are indexed and have meaningful descriptions.