Two claims circulate about checking your own skin. One says it is pointless, and the other says it replaces an exam. This article reads two named medical sources, the American Academy of Dermatology and the American Cancer Society, on how to do the check and how often.
How the American Academy of Dermatology describes the mirror check
The American Academy of Dermatology gives a plain method: "Examine your body front and back in a full-length mirror, then look at the right and left sides with your arms raised." It is a set of steps, and it asks for no equipment beyond a mirror.

How often the American Cancer Society says experts suggest looking
The American Cancer Society says, "However, many doctors and other experts recommend checking your skin regularly, often once a month, to help you notice any new or changing spots." The goal it names is noticing change, which is a different job from diagnosing a spot.
While you check, the Skin Cancer Foundation's page on melanoma warning signs and images gives you something to compare against.
A mirror check and clinician screening are separate
A look in the mirror is your own observation. Screening by a clinician is a separate question with its own evidence, which the National Cancer Institute lays out in its patient summary on skin cancer screening.
Keeping a note of new or changed spots
Note which spots are new or have changed, since that is the goal the American Cancer Society names. Bring that note to a clinician and let them judge it. The Skin Cancer Foundation's skin cancer pictures can sit open beside the mirror, though no photo can diagnose a spot.