Answer: How you approach your project will depend upon how long you plan to live in the rental. If it's just a year or two, I'd suggest gardening in containers rather than trying to rework the neglected yard. If you plan on being there 3-5 (or more) years, then you can recondition the yard without feeling as though you've wasted your time and money.
There are many, many different kinds of containers, from pots to long boxes. As long as they are at least 12" deep, you can grow shrubs, flowers, vegetables and dwarf trees. You can even hang flowering baskets from the limbs of the existing trees. When it's time to move, you can take your garden with you.
If you'd rather work the ground and plant a garden, you'll want to remove any rocks that are fist sized or larger then add some organic matter such as compost. Dig it in to a depth of 8-10 inches, level it out and broadcast some grass seed or plant a groundcover (ajuga, wooly thyme, etc.) Groundcovers won't need mowing and will help hide the rocks and stones. Or, you can remove the rocks and add some topsoil to the area and then plant grass.
Best wishes with your garden!
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