Watch the scene that you plan on analyzing at least once before you begin to make any formal observations.
Consider why the scene is important. Note the tone of the scene, and how the scene moves the narrative forward, if at all. Make sure you understand what happens in the scene with regards to the film's story and plot.
Focus on the dialogue in the scene. Perhaps there is no dialogue. If this is the case, ask yourself why this is so, considering whether other sounds fill in for dialogue and what the importance of sound effects in this scene might be. Think about all of this in relation to the plot.
Annotate the shot sequence in the scene. This is akin to taking notes in the margins of a book: note how the scene begins, how it continues and how it ends. Does it open with an establishing shot or an extreme close-up? Is there a dissolve from the previous scene, or a cut from black? Are there any dolly movements as the scene progresses? How long is each shot held?
Review the annotations that you made, and look for patterns and variations. Consider how the patterns -- or, in certain cases, the lack thereof -- might communicate a message. Consider whether they add tension or levity, and why. Think about why the director would have chosen to edit this sequence in such a way and how it affected you, as a viewer.
Observe how well the scene is lit. Is it dark, or very bright? If the film is in color, how vivid are the colors? Are there any unusual or unnatural colors? If the film is in black and white, how stark are the colors? Is the scene full of brighter greys and white lights, or darker greys and black shadows? How might all of this add to the mood of the scene?
Listen closely to the music in the scene. Consider how it contributes to everything else you have already observed, if it serves as background music, or if there are any cues that tie in with the events on screen? If the scene does not have any music, think about why this might be the case.
Investigate the film itself. Think about the film's history and its production, and research the work and legacy of the director. Awareness of when a film was made, and understanding the life and concerns of its director, can provide a glimpse into the meaning of the film, which, in turn, can help place the scene you are analyzing in the right context.
Read the opinions of scholars and critics. Many times, they will discuss the director's choices in scene construction and editing; they often analyze particular scenes as well. Their writing can assist you in understanding more about the director and the film, and help you fine tune your own analysis.