I don't have a clay soil problem but I have been very happy building beds using the lasagna method, also called sheet composting. Starting with a layers of wet newspapers (about 8 sheets), I add alternating layers of fresh cut grass, old leaves, and a little bit of wood ashes and other soil amendments. The author also uses peat moss. Figure out what you have available that's free and can be used. The first year I got lots of grass clippings from a neighbor. I top the pile off with a layer of composted horse manure. Source was found on Craigslist. You could buy some manure in bags if you have to. If you have time to build up the pile a season ahead, I would also add a layer of kitchen scraps. I have even used a layer of paper scrap as a brown layer.

What and when you want to plant determines your top layer. I'll plant tomato transplants in a fresh bed but make a whole that I fill with compost. If I want to plant fine seed, I prefer to have built the bed the year before so it is well broken down.

I would use some of your existing soil in the layering. I assume you don't see any earthworms in your clay soil. That should change if you add a lot of leaves, grass, etc.

I have a heavy clay loam. There are lots of earthworms though, so it's not all bad. I built my raised beds this spring by digging the grass out around the edge, building the concrete block raised beds (2 deep). The bottom 8 inches is grass clods and leftover clay soil from other projects, and the top layer is bagged composted manure and peat moss. I'm letting the roots and worms mix it for me. It is not ideal, since I do need to weed grass out once a week and water perhaps 3x per week, but it's working fine so far. My tomatoes are going crazy, I'll have cherry tomatoes to eat in June, in WI! But, with the surface mulched with straw, my garden is growing very nicely using "conditioned" native soil.

I'm not sure what you read that made you so pesimistic. I will tell you that I certainly felt that way to start with. I live in the NC piedmont which stands for a deep vein of red heavy clay soil. White clay is even worse as it indicates that air can't get into the small particles and rust the iron to red. However it is plenty hard and slimy clay like when wet. We have the largest hand thrown pottery community here. Thirty miles south, the soil turns to sand and the interface is the brick capital of the country!

I doesn't appear that anything except grass will grow in this soil. However, if ammended heavily with bulk, it does wonderfully as it holds water and nutrients extremely well. We are in the country. I found a cattleman who has cow manure/bedding piled up and mixed after being mucked out of the barns. I bought a dump truck load (I actually bought two and moved it multiple places later) and had a third to a half of it dumped in my ~25' x 35' garden and tilled it in. That could have been between 6 to 10 cu yds of black composted manure. That changed the texture of the soil and it is still there after 6+ years. Gas was much cheaper then and it cost me $60 for delivery and $50 for the manure. Would be much more now for delivery.

Depending on you location and area, if you can get someone with a backhoe (small) or skid steer and dig out where you want the garden down about two feet fill the hole with what ever compost you wish and put the dug out soil back in roto-tilling it in in layers three to four inches deep saving enough compost to put over the top of the probably now raised area and then roto-till that in.
The plot should drain fairly well after that.

A landscaping company I worked for put bushes in some horridly poorly drained soil and we drilled holes for each bush to be planted in so they would not drown in the ground.
If drainage is serious problem drill some dry wells, with a large post hill auger, filled with river rock at the corners and center of the plot before refilling.

Try hugelkultur.

I just did this with my heavy, grey colored, clay soil.
First time I've been able to grow well, the squash love these beds.

Dug down 1.5 feet. then added logs and partially rotted branches, in layers while filling in each layer with the clay I had dug out. Now it just looks like a raised bed. Didn't add any other soil amendments, just thick pine needle mulch. I did pour a jug(s) of urine on it after, figured the logs would absorb it and decompose faster.

The squash and cukes planted their are very green and healthy.

I have hard georgian clay soil but now its softer than before because i put in some cheap mircle gro soil conditioner and some sand be sure to till the soil to a point of a foot or so then add some lime and more conditioner and sand if it doesn't suit your soil wants but it will a take a year or two or more depending on the cash in your pocket. Remember a tiller helps a lot!!!!!!!!!!!!!!!!!