Unfortunately, images are hard for search engines to create search results for. There are some clues of course.
Here is what can be done.
1] The image alt text. The alt text should be a sentence with a subject, predicate, and object to allow better semantics analysis. Make the sentence as reasonably verbose as possible and not overly simple or too complex. The important thing to remember is that the alt text is to help users and describe the image. Make sure that you are not thinking in terms of keywords and rather about describing the image with simple language.
2] Images in content. Google and others use the content blocks around the image to understand the image. A content block is each paragraph and sets of paragraphs (taken as individuals and as a group) following a header tag. Header tags are important too. This means where an image exists, the one header tag above the image and the paragraph before and more importantly following an image are taken semantically to help understand the image. When the image alt tag and the semantic blocks agree semantically, these are taken as clues. For example, if you are talking about hunting dogs and describing popular bird dog breeds used in duck hunting, following a paragraph describing the pointer breed, an alt text like Bo, an International 2014 Champion Pointer dog, is a popular bird dog breed for duck hunters in North America and in Europe. would work semantically to indicate what the image is about and allow for a greater search capability. It not only indicates a pointer dog, but allows for searches such as popular American duck hunting dogs.
3] Keep in mind that capitalization is also a clue. Do not make your sentences all caps or capitalize terms that do not make sense, however, you should capitalize terms of importance that make sense. Do not try and game the system, but use this tactic appropriately like I have in the example.
4] If you do not mind direct links to your images, you can offer a link directly to the image. In this, the link text is also important and should also be a sentence with a subject, predicate, and object. It should follow the example I gave earlier in the alt text to enhance the understanding of the image and increase the search potential of the image.
5] One other option is the figure caption tag. While it is not clear how much effect this tag has on search, I would be willing to bet that Google pays attention to this tag. It would make sense. You can see how to use the tag here: http://www.w3schools.com/tags/tag_figcaption.asp Again, use semantics to your full benefit.
6] URL/URI path. You can place the image in a directory that describes the image. In this, you will need to be brief such as */images/bird-dogs/popular/pointer/. Do not get carried away. This is one case where simple is best.
7] Image file name. You can name your image according to what it is. Again, you will need to be brief such as pointers-are-a-popular-breed-bird-dog.jpg Again, do not get carried away.
On-page clues listed in order of semantic importance: the page title tag, the link text, the image alt text, the content blocks, the one header tag above the image, URL/URI, file name.