According to Young, the following steps should be taken when dealing with a patient possibly in a coma:

Perform a general examination and medical history check
Make sure the patient is in an actual comatose state and is not in a locked-in state or experiencing psychogenic unresponsiveness. Patients with locked-in syndrome present with voluntary movement of their eyes, whereas patients with psychogenic comas demonstrate active resistance to passive opening of the eyelids, with the eyelids closing abruptly and completely when the lifted upper eyelid is released (rather than slowly, asymmetrically and incompletely as seen in comas due to organic causes). Find the site of the brain that may be causing coma (e.g., brainstem, back of brain...) and assess the severity of the coma with the Glasgow Coma Scale
Take blood work to see if drugs were involved or if it was a result of hypoventilation/hyperventilation
Check for levels of serum glucose, calcium, sodium, potassium, magnesium, phosphate, urea, and creatinine
Perform brain scans to observe any abnormal brain functioning using either CT or MRI scans
Continue to monitor brain waves and identify seizures of patient using EEGs

Initial evaluation
In the initial assessment of coma, it is common to gauge the level of consciousness on the AVPU (alert, vocal stimuli, painful stimuli, unresponsive) scale by spontaneously exhibiting actions and, assessing the patients response to vocal and painful stimuli. More elaborate scales, such as the Glasgow Coma Scale, quantify an individuals reactions such as eye opening, movement and verbal response in order to indicate their extent of brain injury.
A coma is a deep state of prolonged unconsciousness in which a person cannot be awakened, fails to respond normally to painful stimuli, light, or sound, lacks a normal wake-sleep cycle and does not initiate voluntary actions. Coma patients exhibit a complete absence of wakefulness and are unable to consciously feel, speak or move. Comas can be derived by natural causes, or can be medically induced.Clinically, a coma can be defined as the inability consistently to follow a one-step command. It can also be defined as a score of ≤ 8 on the Glasgow Coma Scale (GCS) lasting ≥ 6 hours. For a patient to maintain consciousness, the components of wakefulness and awareness must be maintained. Wakefulness describes the quantitative degree of consciousness, whereas awareness relates to the qualitative aspects of the functions mediated by the cortex, including cognitive abilities such as attention, sensory perception, explicit memory, language, the execution of tasks, temporal and spatial orientation and reality judgment. From a neurological perspective, consciousness is maintained by the activation of the cerebral cortex—the gray matter that forms the outer layer of the brain—and by the reticular activating system (RAS), a structure located within the brainstem. Etymology
The term coma, from the Greek κῶμα koma, meaning deep sleep, had already been used in the Hippocratic corpus (Epidemica) and later by Galen (second century AD). Subsequently, it was hardly used in the known literature up to the middle of the 17th century.