You'll need to take some pictures to your local nursery to determine the grass type. Then, they can sell you seeds for the patch and explain what the grass needs or what happened to the area. This, is most important because grass seed won't get rid of disease (burns the grass out), pest infestations (eats the grass and its roots away) or water pooling in low spots (rots the grass).
- The dead or dormant area is a symptom of a, possibly, bigger problem or it may have just been where the previous owner tied up the dog, whom wore or pee'd it away. Female dog urine can kill most grasses due to its high nitrogen content or most any dog on a high protein diet. The best course of action may be to get rid of the old grass and go with a grass that's hardier or easier to maintain...sod instead of seed is the quickest turn-around.