If the garage has lengths of wood use them to mark out rectangles for digging and do a piece at a time. It is easier and takes less time to do a small piece. Then it is completed and you have the first done. Ready work out your mistakes then do not make them on the second, third, fourth...
Throw some seeds in, preferably a bit more ordered then ramdom scattering. But whatever you feel like.
Also means that in the future, if wanted, you can mark the beds off, enclose and convert to raised beds.
As to the soil, dig in just about anything that will lighten the soil. Manure, spend potting compost. I have used fine bark chips and similar fine mulching material, add some course sand and grit. The aggregates that Wickes sell is pretty good.
What to start with, keep it easy. Onion sets (white onions) are fair, turnip, swede, parsnip, garlic, leeks, tomato's. Carrots need an easier soil then you describe, try these in large pots then next year add the compost to the beds, dig that in again.
If find I get better results from potato's in large pots then from in the ground. So I grow 3 larde pots of potatos (50cm pots) and agin the used compost gets deposited on the garden afterwards. Problem is you need to add manure to the pots as the compost isn't enough.
Try potato's in the ground as you want, if OK carry on, mention it as I have had little success in the ground.
Get a small fork, turning over a small forkfull of heavy soil is easier then a large forkfull.
Don't worry about the worms, they will appear soon enough. They like leaves apparently.