Hugh is absolutely right, but just to add a bit more explanation…
Nominative is the "default case" in Latin. If all else fails, use the nominative. It's also, conveniently, the form listed in dictionaries, and the form people will use when talking about the word itself ("The Latin word for 'lord' is dominus").
Accusative is used when it's the direct object of a verb. In other words, when there's a verb, with a subject, and the subject is doing something to your noun—that's when the noun becomes accusative. Unlike in English, this can even apply to verbs with passive forms, like Marcus sequitur canem, "Marcus is following the dog".
In your first sentence, nothing is happening to the dog: the verb "is" doesn't represent any sort of action. Since nothing is making the noun accusative, it'll remain nominative.
In your second sentence, though, the verb "want" is happening to the dog. It's a direct object, so it becomes accusative.
Note that, as Joonas notes, these aren't quite the same rules as in English! In English, any verb makes a following noun accusative, even verbs like "is": consider "he is my favorite person" versus "my favorite person is him". If you ever hear an exchange like "Is Alex here?" "This is he.", that's a prescriptivist Latin influence rearing its head.