I use cardboard. A few layers of cardboard and newspaper will shade out the grass and balance the C/N ratio to some extent. I usually put wood chip mulch on top of that and in 1 year everything under the wood chip mulch will be decomposed. You need to cut holes through the cardboard to plant but that's not too difficult. If you're having trouble, make it wet and tear it with a shovel. You also need to water deeply around the base of the plant but you should be doing that anyway.
You can get cardboard in bulk for free at grocery stores, etc.
I've used this method to wipe out a canada thistle infestation once. Canada thistle is very difficult to vanquish because it spreads by rhizomes as deep as 6' underground. One time I dug out all the roots for the first foot of soil and it came back. I even think I heard it mocking me.
I prefer this no till method because it doesn't disturb the soil biology (worms, bacteria mycorrhizal fungi). Trust me, you want that stuff in your soil.