To create a vegetable patch, you might follow these steps:
1. Take a rope or string and lay it on the ground to mark the planned patch.
2. Take a spade and cut lines vertically and horizontally with about 1 ft distance.
3. Remove the grass patches of about 1 sq ft size by using a shovel.
4. Now dig up the cleaned soil with your spade – 1 to 1,5 ft deep.
As the soil is quite hard as you said, water the planned patch thoroughly and wait a moment after that.
The soil should be easier to dig afterwards.
5. While turning over the soil, mix it with compost (two liters / 9 sq ft) or, if you have some, take manure (one wheelbarrow full for 90 sq ft). If you use sacked compost from your garden center, follow instructions of the producer.
6. Special hint: If your soil is hard due to clay, you will get it smoother by mixing sand into it.
7. After digging, wait two weeks (or a rain shower) for the soil to set.
8. Then rake the bed an divide it in different parts for different vegetables.
According to experience, each bed of the patch should be four feet wide, with a path of 1 to 1,5 feet width between two beds to walk through.
You could also create a little passage of four feet width to easly reach the middle of your bed from both sides.