How many months old is a one year old dog in dog years?

Depends on the breed and which definition of "dog year" you use.

By the definition "the amount a dog ages in a year", the answer is simple: 1 year.

By the definition "the equivalent portion of a human's lifetime", for larger breeds it's about 9 and for smaller ones about 13 (according to Wikipedia).

The popular formula "1 dog year equals 7 human years" (or vice versa) is inaccurate.