This is one method of analyzing photographs, based on the Library of Congress Teacher's Guide to Analyzing Photographs and Prints. You'll learn about different methods and frameworks for analysis during your studies, so find one that works for you, or take elements from different ones.
Investigating a photograph is not a linear process, it is cyclical. Observation, reflection, and questioning do not happen one after another. It's a cyclical process where new reflections lead to new observations which lead to new questions, etc.
Here are some prompting questions to help you observe, reflect, and question:
What do you notice about visual elements?
What do you notice about design principles?
What do you notice first/last?
What's in the foreground, middleground, background?
How is everything arranged/composed?
At what distance or viewpoint did the photographer take the photo?
What is the lighting like?
Is there text? What is its relationship to the image?
Why do you think this image was made?
What’s happening in the image?
Do you think the observations you made were done intentionally by the artist?
Who do you think was the audience for this image?
What tools were used to create this?
What themes can you draw from the image?
What can you learn from examining this image?
What’s missing from this image?
What other images could add context to the image? Is it based on someone else's work?
What can you tell about the photographer's style and point of view? How does it fit into their overall portfolio?
Is the image a reproduction or is it edited?
When you're done observing and reflecting, think back to the list of questions above and try to remember anything you're leaving out.
What don't you know about the image?
When do you think it was made? Do you think it was received/interpreted differently then?
One way to organize your analysis of an image, or of an artist's body of work, is to map it! Here is an example, but feel free to try different ways of organizing your map to fit how your brain processes information.
Definitions taken from "Collaborative Learning using Concept Mapping," by Patricia Lupion Torres & Rita de Cassia Veiga Marriot