Your best bet is to try loosening the soil, I had the same problem making a raised bed near my house, the soil was nothing but clay and extremely compacted. I mixed compost and tilled it with the clay (tilling is bad but you don't really have a choice with hard compacted clay and if you're impatient). Another thing you could do is get saw dust from untreated wood and sand and mix it into the soil to help loosen the soil and improve the drainage. This should make your soil rich from compost; loose and well draining while at the same time good at retaining moisture from the compost, sand, saw dust, clay mixture.

Your soil is clay and the solution to clay soil is organic matter. Adding more soil to that clay is not a very good solution since what ever you do add most likely will be 95 percent mineral (that is what clay is) and 5 percent organic matter.

I feel your pain, just went through this process myself. Kimmsr is correct. Tons of organic matter, mixed thoroughly as deep as possible. ROOTS are the name of the game and they HAVE to be able to be able to penetrate soil easily for a vigorous plant. I broke the hardpan (wet) with a shovel. Did'nt turn it over, just fractured it. Threw on about 5 or 6 inches of a premium planting soil/mix (mostly composted yard debris) I bought for 35.00 a yard from a local landscape supply and rototilled it in good. Be aware that with the additional humus your ground level (grade) will rise. The results came out dark, rich and friable. This was done to 5 flowerbeds three weeks ago and the misc flowers we planted are exploding.
These beds will compact over the seasons I'm sure but will turn and crumble easily with a spade nxt spring. Good cardio exercise and satisfying results. Pour the OM to it!

You could rent a tiller. Some say not to till when the soil is wet, but completely dry clay can just be too hard to work. I soak the ground with a sprinkler or a good rain, and then ~2 days to a week later till and dig the soil with a shovel. Add as much compost/manure/OM as you can, either before or after the first pass with the tiller and mix it in. You can also use a shovel, either instead of or in addition to the tiller, just more work and takes longer. You don't need to remove any soil, the raised bed will help with drainage and it will settle and shrink back down over time.

Till in tons of organic matter, any that you can lay your hands on, even if it is wood chips (in this case, you my have to fertilize with nitrogen for a time). For me, leaves work best. Consider at least six inches of OM on all property, to be tilled in, although frankly I would start with one foot if possible.

Alternatively, dig big holes and bury large, rotting logs or branches (hugelkultur). Large logs do not produce the same N-deficiency effects that sawdust or chips might produce. Then wait.

I've always gardened in clay, so I understand your challenges. The only thing I can add to the good advice you've already gotten is that there is a bright side. Once you get it loosened up enough to plant in you will end up with a fertile base that beats out all others. Clay is extremely nutrient rich!