I grow all my veg in 10 raised beds. Basically if you have heavy clay soil you need to add plenty of compost which you need to initially dig or rotovate in for starters. I bought myself a cheap electric tiller which does the job so quickly & is light to handle. This will open up the soil structure allowing beneficial air to enter. Avoid treading on or compacting your soil, use boards if necessary to stand on to spread your weight when planting & harvesting etc.
Each year top up with a layer of compost, I use an old fashioned three pronged fork to simply dibble it into the top couple of inches.
Other than that it's simply a case of weeding with a hoe throughout the growing seasons.
I never use a spade to dig my beds so I guess I'm as near to a 'no dig' garden as is practical but it took abit of work initially to get to this point. Good luck.