What are you using for equipment? This does not sound like a stabilization job, rather a modification. Thats splitting hairs, the dividing line is based on % of material added. I assume you have a soils engineer for the project? If so, get with them. Base your amount a portland needed on your moisture content. Lime will work, but it is usually more costly than portland, and it has more handling downsides, IMO.
Our normal process for small stabilization was as follows. Assuming you are getting the load of portland delivered in bulk, you will need a big roll of heavy plastic. Dig a small pit, sloped deeper on one end, this will help you with spreading later on. Put dirt on the edge of your plastic, leave a few areas on each side where air can escape. Have the tanker driver get his hose as far under the plastic as possible. Have him blow the load off with low pressure and as much volume as he can. This will reduce dust.
We usually spread the wet material over the fill area. Then using a backhoe, or loader we would grab a bucket of portland and start spreading it thinly over the wet material. If it is extremely wet you start nearest the pile working your way across the fill. This will help give you somewhat solid ground to drive over. If its dry enough you can move across without getting stuck, then go all the way to the other side of your fill and spread in reverse. This seems to spread the material a little more evenly.
Mixing the material in. This always depending on how many sq ft we had to do, how wet the material is, and how well we needed the material blended. Im going to take it this job is small. Your best bet, if you have enough room is corner the blade of a dozer and roll it into the clay. Then windrow from one side of the fill and back again, at least twice. This will help blend the material in. If you can get a rototiller on a small tractor this will work well also.
Now here is where things are tricky. This is more art than science. Depending on how wet your clay actually is, you may need to add water. Sounds back asswards when youre trying to dry material. But the portland needs moisture to start working. If after blending your portland, the clay looks more like sand and is granular, you need more moisture. If it looks like a load of dry clay picked up with a self loading scraper, youre in good shape.
Compact, and grade as normal. Remind your soils guy that the moisture level on his density gauge may be a little higher than it should be for the material and proctor, have him come back a few days later. Remember, portland will burn you, its not as bad as lime is though. You get some lime in your boots and sweat a little, you will have a real hot foot. Common way we tested our lime to see if we had a good hot batch, was to mix some lime with water in a plastic pop bottle, toss it away and watch it blow up. I would also say, be prepared to clean your equipment. It is a dusty job, and if your machines have any moisture on them, the cement will stick right away. A good washing will take care of this. Also, be prepared to replace air filters on your machines.