What do you write when you sign a letter on behalf of someone?

The usual is p.p. - which stands for pro percurationem inLatin

Name , street address and name, city ,state and Zip code.

Generally, you would be asked to do either a personal reference, or a professional reference.For a personal reference, you want to say something about the person's character, and maybe an example or...

Only if they have Power of Attorney over you. Power of Attorney is usually only awarded when a person is no longer capable of making their own decisions. Also, parents have a limited ablility to sign...

you need a power of attorney in order to do so