You can enjoy the taste of homegrown vegetables even if you don't have (or want) a big garden. Start with a container that's at least a foot deep and about a foot wide. Fill with soil to within 1 inch of the top and add seeds or young plants. Try putting more than one kind of vegetable in a pot for a pretty growing salad. Leaf lettuce is easily grown in a container. It doesn't mind being in partial shade, and if you place near your house, you can pick the outer leaves for your salad, while encouraging further growth. Cherry tomatoes also do well in a container. You might even want to try them cascading from a hanging basket. Place in an area that gets at least six hours of sun each day.
Taking care of your container garden is simple and fun! Place it in an area where you will pass by often. Check your plants every day to see how they are growing. Just as plants have different sun requirements, not all plants benefit from being watered every day. Check the soil. Plants in containers do tend to dry out more quickly than those placed in your garden. Most plants do best when watered as the soil begins to dry out. Very few plants do well in soaking wet soil.
You and your children might enjoy keeping a gardening journal. Allow at least one page for each plant you grow. Your children can draw the plant, using the seed packet or a gardening book as their guide. Together you can track its pattern of growth, record how long it takes to spring up from under the soil, how long until it blooms, and if a vegetable, how long until harvest. Over time this will also help you figure out which plants work out best for you, rather than leaving everything to memory. So dig in, and get started on container gardening.