Where do you live?
Do you have a type of grass in mind?
Is this area shady?
How big is the dog and how active?

I'm in northern Michigan, zone 5. I do have it in my profile but for some reason it doesn't show up by my name.

Small dog - shih tzu/cairn terrier mix. He isn't outside all day, just to do his business or play, chase chipmunks or whatever. He has a tendency to run off (was a shelter dog), so that's why I need to put him in the fenced area.

I call it a dog run because it had a kennel in it, which I gave away, but it's really the whole side of my house, which is about 50' x 30' and borders the woods. I want to make it an extension of my yard.

As for grass, I don't know what kind. It gets about 50% sun. Any suggestions?

if you are in a rural area you should consider what you will be loosing with a dog in the yard. When we moved in two years ago our neighbors had two large dogs in a fenced area of their back yard. This spring they moved out and took the dogs.

While we would occasionally see deer before they left, we are now seeing them on nearly a daily basis. Yesterday a doe and her twin fawns came into the yard where she nursed them. The fawns are only about 18" high, not much taller that the small azaleas we planted last year.

For the last month we have had a young hawk in our yard on a daily basis. I was surprised at the number of insects the hawk eats, I had always consider them eating mice, birds, etc.

While dogs are nice, having the deer, hawks, squirrels, numerous different small birds makes the back yard pleasant.

Wait until mid August to start this project. It is too hot now.
Fescue is the only grass choice for that much shade. It is not very forgiving of dog digging or wear and tear so just know that in advance. Get the project going in August to give yourself time to add more seed if you see thin spots.

1. Fertilize the weeds so they will die quickly
2. Kill the weeds with Round Up which will kill anything it gets on
3. Water the area every day as if you were trying to sprout seeds
4. After a week of daily watering, spray the new weeds with Round Up.
5. Wait a few days, rake up any dead foliage, and seed. Roll the seed down with a water roller to make good contact with the soil.
6. Water 3x per day for 5 minutes to keep the seed moist. Fescue seed should spout in 2 weeks.
7. Mow when the new grass is 4-5 inches tall. Mow it down to 3.5 to 4 inches.
8. After you have mowed for the second time, you can apply a synthetic fertilizer. Or you can apply organic fertilizer any time.

After you have mowed the grass once you can start to back off on the frequency of watering and increase the duration. By that time of year your goal will be to water 1 inch of water, all at one time, every 2-3 weeks. It might take some time to get there but that is the goal. Next year you will gradually move from monthly watering up to weekly watering as the temps increase.

Thank you dchall, I appreciate the advice. Will save these instructions for later in the summer.