A man has a disease caused by a dominant allele. The mother has the disease but the father does not, explain how we know the man is heterozygous for this disease.

So first we must gather the informaton, the disease is caused by a dominant allele, we may call this 'D', the recessive could therefore be 'd'. The mother has the disease, but the father does not. Therefore the mother must carry the dominant allele, she may be 'D, D' or 'D, d'. The father must be 'd,d' , carrying both recessive alleles otherwise he would have the disease. 

One can then draw out two punnet squares, with both of the mother's possible genotypes. (I can show this using the whiteboard). When you do this you will find that the son must be heterozygous otherwise he would not display the disease, and we know from the question that he has the disease.