A veggie patch is a must for kids.
Start off with an area of about 1 square metre. It doesn't matter what method you use but I prefer to use a no-dig method for a small area.
You'll need a frame about 200 to 300mm high, preferably made from timber. Don't use treated timber. It may have been treated with poisons, which could leach into the soil.
Start off by covering the ground, which could be an area of lawn, with a generous layer of manure and give it a good soak. Cover the manure with a layer of wet newsprint, at least 1 newspaper thick. Make sure the newspapers overlap each other. This will kill the grass and weeds and prevent them from growing again. There's no need to dig because the manure and newspaper layer will help the weeds/grass to break down and will also attract worms, which will work your soil for you.
Place the frame on top of the newspaper and fill the frame with compost. Give the compost a good soak. You can then plant seedlings directly into the compost. If you want to sow seeds, make a small hole in the compost and fill the hole with a good organic seed raising mix. You can then sow the seeds into the seed raising mix.
The compost will continue to break down and settle over time, so you'll have to keep adding more compost.
See the vegetables and herbs sections of this web site for growing instructions.