Well, if they have Type 1 diabetes, they will usually know very early on that they are "different" from most kids. For example, a 3 year old might realize that they need to get a "needle" before they eat, while their friend and sister does not. Once they start asking about their diabetes care, it provides a good opportunity to explain it to them in very simple terms.
You might say something like "Mommy has to give you your medicine to keep you healthy so you can grow to be big and strong".
To an older child (age 5), you might say: "Your body does not make insulin anymore, so you have to inject the insulin your body no longer makes in order for you to stay healthy. This is called diabetes". Most kids by this age can help with basic care, like cleaning their own finger for a blood sugar check. Giving them some control will avoid you having to chase them down when it's time to do a shot. In most cases, anyway!
There are many books out there and videos for kids with Type 1 diabetes. There is also Rufus, the diabetic stuffed bear. There are other "diabetic dolls" that can be used to show kids different injections areas.
It's a good idea to get the child involved in local day camps and programs for diabetic children. They can meet others like them, and learn more about age appropriate diabetes care. Most kids can attempt their own injections by age 10 or so. However, the parent should still be in charge of the actual drawing up and dosing of the insulin.
If the child has Type 2 diabetes (Used to be unheard of in kids, but is becoming now more common due to childhood obesity), you might want to focus on *actions* more than words.
Make the entire family eat healthy meals, and exercise together. You can tell the child that they need to eat healthy and exericse to help keep their diabetes under control. Explain that their body doesn't use the insulin they make they way it should, but eating the right foods and getting out to play can help make that better. Many of these kids simply don't know that Pizza Pops are bad for them.
Diet and exercise are the cornerstone of Type 2 diabetes management. In many cases, kids who develop Type 2 can treat it with diet and exercise alone and keep it at bay, provided it is caught early and they lose any excess weight. You need to stress "healthy living for life". Type 2 diabetes is usually preventable in kids, and it does not usually progress if caught early AND proper changes are made and stuck with.
Although when I first went into the hospital as a toddler with a blood sugar of 600 I wasn't able to know what was happening to me (I just remember being put in a cold metal crib with an IV and crying and trying to get out), I was lucky that a new diabetes clinic for children had just opened in my city. So I received excellent one on one care from very early on, and lots of education as soon as I was able to interact.
"Diabetes care teams" consist of a dietician, Diabetes Nurse Educator, endocrinologist, and social worker, and are often used to treat children and young adults with Type 1 diabetes in special clinics. They are the gold standard for care.