Should I say dog or dog? - briefly
Use "a dog" when referring to any single, unspecified dog. Use "the dog" when referring to a specific dog that has been previously mentioned or is understood from context.
Should I say dog or dog? - in detail
The choice between using "a dog" and "the dog" depends on several factors, including definiteness, specificity, and familiarity.
When you use "a dog," you are referring to an unspecified, non-specific dog. This indefinite article is used when the listener or reader does not know which particular dog you are talking about. For example, "I saw a dog in the park" implies that there could be many dogs in the park and you are not singling out any specific one.
On the other hand, using "the dog" indicates that both you and your listener or reader should understand which particular dog is being referred to. The definite article "the" is used when the noun it precedes is specific and known to the audience. For instance, "The dog is barking again" assumes there is a particular dog that both parties are aware of, perhaps a pet or a well-known neighborhood animal.
In summary, use "a dog" when you are talking about any dog in general or one that your listener might not be familiar with. Use "the dog" when referring to a specific dog that your audience can identify based on prior context or shared knowledge.