Re-grading yard/drainage

I have horrible, sticky clay soil -- compacted and full of weeds. I'd like to
till and re-mix w/ sand and/or loam -- but also need to change the grade slightly to allow for better drainage. Anyone ever tackled this before?? What materials/tools were used? I wonder if I'm naive,thinking my husband and I can tackle ourselves -- but contractors typically charge around 5K for this kind of job -- so we're motivated! Any help/advice is very much appreciated!

First, does house have enough elevation, so that you can provide down slope? Second, design landscape to have shrubs, tree, etc, because it lessons turf area & adds beauty. Third, farm tractor with hydralic lift in back and soil working implements will do the work. One implement look like a rake with 12" tongs, and can tear into compacted dirt. Fourth, you need to take off 12'18 inches and then add back that much in black dirt. G'luck