I'm out of the clay now, thankfully, but I always added lots of peat and compost, and some manure (not as much as I would have if it had been free), both at planting time for perennials and yearly in the veggie garden. Whatever 'roughage' you can add is going to benefit the soil.

I'm always adding compost, peat moss , leaf mold etc. and some aged manure. I'd add more if I had a free source.

In addition to what the others have added I also amend my soil very heavily with grass clippings and leaves. Boy does it make a huge difference to add these two amendments and there free. he he. I have very heavy clay also and unfortunately, you will always need to add amendments to keep your soil friable and healthy.

Grass clippings decompose quickly. What they really are is a good source of nitrogen needed by the microorganisms that break down organic matter. So it is a most excellent compliment to other organic materials.

Any organic materials or compost is great in clay, and you can't get too much. Peat and manure do different things in the soil. Use both. When you use manure, realise if you are using manure, or a compost/manure mix. Both can be good, but the compost/manure mix is usually 10% or less manure.