- Remove the grass (manually or with sod cutter), add loads of compost and till. This is truly the best method. If you're in an older neighbourhood, your soil is probably hard-packed under there. If you're in a new neighbourhood, you probably have only 6" of topsoil. Take the time now to prepare your soil and you will thank yourself for it later.
Kill the grass (a. smother with carpet or plastic for a season, b. smother with newspaper and top with a mixture of topsoil and compost, or c. use herbicide and top with soil)
For method a, wait for a year before planting - but it doesn't look pretty in the meantime! Also, using plastic will kill all the beneficial organisms in the soil.
For methods b & c, you can plant right away by digging extra-large holes to amend the soil on a plant-by-plant basis. This works too but is more work in the long run. Also, in our dry climate, it takes a while for the newspaper to break down (supposedly you can cut through it with a shovel when you plant, but it's been a headache whenever I've tried it). I don't recommend herbicides for environmental reasons. Besides, in both cases, you'll be raising the soil level and will constantly having soil falling down onto your sidewalk or patio. If these disadvantages don't bother you, look for more details by googling "lasagna gardening".
Build raised beds If the raised bed is at least 8" high, it will take care of the problems of compacted soil or lack of soil as well as soil falling where you don't want it to. There are many beautiful options to match your house and garden style to contain the raised bed - stone, wood, brick or concrete blocks and more. Put the newspaper down to prevent grass growing through, and fill with a quality garden soil mix.