Add organic material, compost, well rotted manure, leaf mould, whatever you can get hold of. The more the better!

As above.....absolutely anything from well rotted manure to grit to spent potting compost to rotted kitchen waste.

It might also be worth the effort to really dig it deep during the autumn and let the winter weather get at it to break it down

Hi Billyc and welcome to GoY. As above plus spent mushroom compost and composted bark (if you can get).

As a last resort next year pile your lawn mowings about a foot thick (if you have any)on one or two of the worst areas. By the spring the pile will have shrunk down and you can dig it in. It does improve the texture though you might want to add a bit of general fertiliser as the rotting process can deplete the nitrogen content. For this year if you want to plant you could make the planting holes bigger than normal and fill in with good compost instead of garden soil.

Improving poor soil isn't a quick process. Plant robust things for now.