When making a new bed. We till early in the spring, again a couple of weeks later and again a couple of weeks after that. We keep tilling every 1.5 - 2 weeks until we plant. It helps kill off the grass.
When I plant, I dig up the row or hill deep and remove all the grass roots before planting. I take that opportunity to dig in some manure too.
When the plants start growing, I then cover the spaces between plants and between rows with cardboard or newpaper and mulch on top.
If using newspaper, keep it thick, at least 6 layers of paper. It takes a lot of newspapers but just one layer of cardboard.
If possible, I till up a new area a few times in late dry summer, then cover the entire thing with cardboard and mulch and just let it sit until spring, layering manure and kitchen compost and garden compost on top as the season and winter goes along. When spring comes, it's a great bed to plant in with very little work.
I made a new bed this year for additional things and a new strawberry bed. I tilled well first, dug up the rows, cleaned them out, dug manure into the rows and planted. Now I am focusing on covering the open row areas with cardboard/paper and mulch, when I can get it. Getting enough material can be hard. I live near the industrial area of town, so make a short trip through there on recycle pick up day for cardboard and shredded computer paper. Shredded computer paper makes great mulch if it's the little stuff. The big stuff just blows away. It's a wood based product and works well to keep the weeds down. It just looks odd, being so white. lol! I always add manure when I plant, to counteract the nitrogen loss from the paper decomposition.
Sometimes I have to turn the sod over to keep the grass down until I can get paper and mulch on it. Those grass roots are nuts!
This year I tilled a grass perimeter around all the gardens. I intended to keep it tilled throughout the summer but we'll see how that goes. It's a new idea. I may decide not to use the fuel. It's getting expensive!
Grass is always a problem. It's a continuous battle. The cardboard and mulch have to be continually replaced to keep the grass and weeds at bay and the edges of the mulched garden have to be dug to keep the grass out - but it's easier then hoeing everything.