New to gardening and ugly lawn?

I am new to gardening and just moved to a new house. Our back garden is patchy, weedy and full of small stones. The soil is greyish colour, not sure if that is normal. We have mowed it a few times, raked it, stabbed the soil with pitch fork and lightly covered lawn with lawn fertilizer then watered it. Over a month later, the lawn hasn’t improved. I am aiming for nice green soft grass. Any tips?