Ah yes, the eternal problems with creating a garden; ridding the grass and weeds.
Here is what I do: I use a shovel and lift the entire root system out of the soil and flip it upside-down and then break the sod up with the shovel. Here, it composts in place and no nutrients are lost from the soil.
Now, once and while some grass will come back but on the whole this method actually works quite well. When grass does poke up again, just use the shovel to break that piece off and flip it over again.
Also, another method is to place black and white newspaper (no colour articles) over the grass (I'd still flip in first) or leaves (C:N ratio for Newspaper is 2000:1 and or leaves is about 300-400:1 and leaves also contain a myriad of micronutrients) over the grass followed by a green (cofee grounds, manure, grass clippings)
ASIDE: A C:N ratio of 200:1 means that the newspaper will decompose much more slowly than the leaves. Also, something to consider is that acids are used to bleach newspapers and reside in the paper which will decease the pH of the soil. (Not by much but, it is something to consider)