Here are some more ideas (I'm assuming that you are the leader and a beginning dancer, Colin):
Try to think more about your partner's feelings than your own. Focus on trying to make her feel comfortable and make her feel that you are enjoying dancing with her.
Don't apologize for your dancing. If you are a beginner, you can say so when you start to dance, so your partner knows what to expect. But if you make a mistake, just keep going and keep smiling. The only time to aplogize is if you step on her (and even if you do, it's happened before, so don't panic).
If it's difficult for you to think of what step to do next during the dance, you might do what some men I know do. Plan and practice a few little "routines" of a series of steps that you know. Then you can use them when you dance and not have to make up the dance on the spot.
Dance at the level you can do best at. I'd rather spend a whole dance doing two or three basic steps than have my leader trying fancy stuff he doesn't quite know and can't quite lead. A lot of guys seem to worry about boring their partners if they don't know a lot of fancy steps, but I think most women would rather dance with someone who can do the basics well and maintain a good connection with her over someone who's trying to dance above his real skill level.
Keep dancing! As you get better, your nerves will get less.