Yes, you can do everything right on top of the current grass. There are several different ways to achieve your goals, but here is what I would do -
Using lasagna style gardening I would build up the areas you want to plant in. Because of this style you will have lower areas, and maybe lower paths which you don't want (see path construction in link below).
So first take note of how the water moves over your front yard. From adjoining lands, from the house, from higher ground. Also how the sun will shine on this area. Then map out how you will capture and hold this water, or at the very least, safely channel it. Here is a neat permaculture rain garden constructed in a front-yard, which may give you some inspired ideas for your garden -
http://www.midwestpermaculture.com/permaculture-125crescent-stelle.php Next, map out your growing areas & paths, and incorporate this into your water movement map.
Now your ready to do some yard work.... using lasagna style gardening build up the areas you want to plant in. Maybe even put some med. branches or large wood chips down on the grass first and cover it lasagna style making Hugelkulturs to plant into. Decide on the material for your paths and lay it down following your map. If you are going to capture/channel water now is the time to dig out your swales, ponds and/or channels.
Planning for sun, water, paths and raised beds (of some type) is what I recommend. The raised bed, lasagna/hugelkultur is how I would deal with shallow soil with uncertain fertility. But to me the water is the most important element to consider first when designing a garden, but then I live in Oregon