I will cut & paste the 'analysing an image' sheet I give to my sixth form group, bear in mind this is not a definitive list!
Composition
Where the critical elements are placed in relation to each other. Whether there is contrast between complementary or contrasting colours or textures. Vanishing points, leading lines or curves & 'balance' of objects. Position of the horizon - whether sky or foreground is given dominance (if it's a landscape). Whether the image follows the rule of thirds or is more symmetrical, or if the subject is dead centre. How the eye travels in the photo. Whether the image is a landscape or portrait orientation or whether it's a square shape. Is the subject facing into or out of the frame, are they on the edge of the frame (or even cropped off awkwardly). Is there space for them to move into? Are they cramped in the frame? The use of negative space. What is the viewpoint of the photographer? Is it eye-level? Low down looking up? Or high up looking down. Is lens distortion or compression evident and how does this affect the viewpoint? Depth of field – is it deep to show details throughout the image or is it shallower to emphasise the main subject whilst still giving context or is it very shallow so the background is a complete blur.
Exposure
Whether the image is B&W (or some other monotone) or colour. Whether it's high key or low key, very contrasty or lacking in contrast. If colour, the extent of saturation - is it bright & colourful or more muted? Is it underexposed, overexposed or is the tonal range equally represented.
Lighting
Think - direction, quality and colour temp. Is it hard, with hard edged shadows, or is it soft with a diffused edge. What direction is it coming from - is it a low angle giving much more texture to the scene or is it from above leading to little or no textural information. Is the lighting warm (golden tones) or cool (blue tones). If you are looking at a portrait of someone is it a known lighting pattern, like broad or short lighting, is it clamshell or butterfly, or Rembrandt lighting. Are there hair/rim lights for background separation? Is it a one light setup or two/three/more lights? Are modifiers used? (You can tell by the direction & the edge of the shadows, whether any fill has been used and possibly the size/shape of the catchlights in the eye (if any).
Subject
Context – is it studio or outdoors. Is the scene busy & bustling or is it tranquil & peaceful?
Finally - what does the image say to you? How does it make you feel? What do you think the photographer was trying to say? Why was the picture taken? Generally speaking, images which tell a strong ‘story’ can be technically inferior – the story carries the emotional impact. For images with less ‘story’, technical perfection is more crucial.