Causes for amnesia can be either neurological or psychogenic. The first implies some physiological damage to one or more of the specific areas of the brain associated with memory, most often around the hippocampus. This can be from a virus like the herpes that left Clive Wearing with no short-term memory capabilities, blunt force trauma, burst arteries or tumours in the brain or the outright removal of certain sections of the brain as in the famous case of H.M. The effects are highly varied; retrograde amnesia (the more well-known type of amnesia - loss of all memory before the inciting incident) as well as anterograde amnesia (loss of ability to form new memories after the incident) have both been reported in different degrees or even in some mixture. Muscle memory and semantic memory often remain, so the patient can still ride a bike and use language, but their ability to learn new skills is more hit and miss. H.M. retained some implicit memory so tasks he repeated often got easier despite it being as if he was doing them for the first time from his point of view. The link above contains an example of this as he grew proficient in drawing a star from a mirrored reflection over time despite his condition.
Sufferers of psychogenic amnesia often display much more localized, selective blanks in their memory, though total retrograde or anterograde amnesia is also possible. These disorders leave no trace in the areas of the brain linked to memory and all seems well physiologically, making it frustrating for relatives sometimes. However, these cases usually result from severe stress, a breakdown or come as part of the package in PTSD where someone involved in a psychologically traumatic event has subconsciously blocked it out of their memory completely. These types of memories can be recovered sometimes using hypnosis or other psychotheraputic treatments.