How we change what others think, feel, believe and do
Appeal to their better nature, asking them to agree just because what you are asking is the kind of thing they would naturally want to do.
Do not make attributions about them or their nature. Just ask. Or even just show that help is needed. When you have said this, stop talking and wait to see if they offer. If they do, then altruism has worked. If they do not, you can still use another method, perhaps initially just asking more specifically.
I wonder if you could help out here...that's great, you're so kind.
Could you do this, just for me? I can't do it by myself.
I'm in trouble here. I need some help, I think.
Using altruism is an assumptive approach where your assumption of their kindness stimulates this response, or at least makes them feel guilty for not helping (so they do help to reduce this feeling of guilt).
It can be a trap sometimes to think you have to use some complex means of persuasion, when all you really need to do is to ask. People like being asked. They also like helping. The need to nurture is a basic drive and we get pleasure from taking the position of the nuturing parent.
There is also a practical benefit in helping others. If they help you, then they know that you will feel obliged to help them in return.
Altruism is the fourth of the 64 compliance-gaining strategies described by Kellerman and Cole.
Kellermann, K. & Cole, T. (1994). Classifying compliance gaining messages: Taxonomic disorder and strategic confusion. Communication Theory, 1, 3-60