| Firstly, I'm assuming your girlfriend is already aware you have diabetes.
The best thing I've found is to just do your 'diabetes' stuff in front of her like it's totally normal. Inject in front of her. Do your BGs in front of her. Treat it as if everyone does these sorts of things anyway. This will make you seem more approachable and then she'll initiate conversations. No doubt she'll ask questions that are loading with misconceptions. Listen to these and let her say them, and then politely but firmly correct her.
If your relationship's going pretty well, stuff will just 'come up' in general conversation. The one thing you absolutely must do though is make it 100% clear that she should NEVER inject insulin into you, regardless of how ill you are or whatever. The problem is that because insulin is seen as the 'medicine' for diabetes, it's seen as the solution to all the problems - and of course the most obvious problem we face as people with diabetes is hypoglycaemia, which is the worst possible time to inject insulin!
Basically the best advice I can give is that if you treat your diabetes and the associated regime as something perfectly normal, those close to you will too.  | 
