Just about everyone can find space for a garden, whether you live on an acre or in an apartment. Step one: Decide where you will put your garden and how big it will be. Gardens can be planted in pots, or plots it is up to you.
Try a theme garden. A salsa garden might have tomatoes, onions, tomatillos, peppers and cilantro. An herb garden would contain your favorite herbs, basil, parsley, thyme, mint, oregano, etc. You might want a salad garden for crisp, cool, summer salads with tomatoes, lettuce, cucumbers, scallions, carrots, spinach. Maybe just a favorite veggies garden is your thing. What theme would you choose?
After you and your children choose the space, and the theme, you will have to go through your catalogues and choose the specific varieties and order them. Be certain you check the planting time and best plants for your gardening zone.
When the seed come you will want to check the packets and find the best time for starting the seeds. Seeds can be started indoors in a sunny location. You can buy containers for starting seeds or you can recycle plastic containers (yogurt or pudding cups, styrafoam cups, egg cartons, cut down milk and juice bottles, etc.). You will need some soil for starting your seeds and the nurseryman should be able to advise you what to buy.
There are lots of resources available to help you with planting and growing information. Search the web for answers to your questions.
This is supposed to be a fun family project. Take pictures of the work and the progress. Make sure everyone gets to participate (hands on). Have the whole family take part in the growing, harvesting, and preparing the food to eat. Young gardeners usually are not picky eaters. Have fun!