Yes it is a small yard. I live in a town house. I was thinking to dig up the whole backyard and put down seed or sod. How can I prevent the weeds from coming up again?

If you use sod, apply a weed preventer product- after the sod is laid. ( many available.....make sure its labeled for lawns) , You can't use weed preventer on seed, because it kills all seeds- good and bad ! Use weed preventer 3 times a year- spring , summer and fall

Kill the weeds first and then evaluate what you have for a soil surface. DON'T DIG UP ANYTHING. That might work for flowers, but it is a mistake for a lawn. Kill the weeds and scrape them off with a hoe. Scrape the high spots off, but don't go crazy and turn them into low spots. I would not scrape down any more than needed to flatten the high spots. The idea is to make a level place for seed or sod. Then put the seed or sod on top of the bare soil. This time is year you cannot seed, because of the summer heat, so let's talk about sod. Set the sod on the soil and walk on every square inch of it to push the bottom of the sod against the top of the soil. Then water lightly until the soil underneath the sod is moist, NOT SOGGY. That will take at most 15 minutes but more like 5 minutes. Keep the soil moist by watering 5 minutes, 3x per day (breakfast, lunch, and dinner time). When the grass gets up to 6 inches tall, mow it down with a string trimmer to 4 inches. You don't need a real mower for that small area. When the sod has knit down to the soil, you can start to back off on watering frequency and water longer. Wean your way down to watering once (at most twice) per week in the summer heat, but water a full inch every time you water. Getting an inch can take hours, so adjust your expectations. The sod will have already been fertilized and will not need more until early September. You may get weeds in the new lawn, but again, wait until mid September to deal with weeds. Summer time is a poor time to spray herbicides because of the heat.

A lawn with as much shade as you have should be mostly fescue (assuming you live in the north) or mostly St Augustine (if you live in the south). Where do you live?

Thank you for the information. I appreciate the help. I live close to Toronto, Canada in a small townhome, that does not get alot of sunlight in the back.

If you are thinking of sod, look for a fescue or blend of fescues. You could do that now or later. Seed, on the other hand, should wait until August for you. If you don't want to do anything immediately, you could start getting things ready at your own pace and seed fescue blend in late August.