How to avoid 'Wasting my Fast'?

I read on an older thread about how one can ensure that they don't 'waste their fast'.

I did not understand exactly what that meant, but I suppose it means don't do X, Y, and Z that nullifies your fasting results..

1) I understand about not bathing with soap or brushing teeth with toothpaste, but what about just pasteless brushing, and showering with no soap? Is that ok?