There are multiple ways to make a sentence negative in Japanese, depending on the politeness of your speech. In the beginning of this course we will only focus on neutral speech, which is polite enough for most situations. This is more polite than casual speech, and less polite than formal speech. You will learn the other forms in later lessons.
Study the table below.
In the question and the responses in the table, note that in the case of a negative question, Japanese speakers say yes to affirm that the situation in the question is the case, that it is indeed not a dog. By responding with no, you deny that the situation the question describes is the case.
This is the opposite of how English speakers use yes and no, so it can be quite confusing. However, when you think about it, the Japanese way is actually more logical.