Well, it’s a matter of using psychology and basic principles to create an experience for the other person that makes them want to help you.  Try these questions:

-   First, why do you want them to help you with this? What purpose does it serve?
-   What is a realistic reward they could expect in return?
-   How much do you think you can influence them? Do they trust you or your suggestions?
-   How do you think they view you? Do they see you as a kind, reliable person who gives good advice?
-   What are their intentions and desires? What is the likely result if they help you? What might be the outcome if they don’t?
assistant
I think some of the first thing we need to be sure of is what you’re asking them to do, and what you’re hoping to achieve.  Because in the end, the way you present your request is going to be a key factor.  You could start with sharing how you’re feeling, in the hopes of sharing empathy, and also letting this person know that you really care about what they think.  
Try to phrase your request as an invitation, rather than a demand.  If you can use ‘I’d really appreciate your help with this’ rather than ‘you should do this’ it can help reframe the request in a way that’s less threatening and less frustrating.  If you start with “I’d really appreciate it if you...” rather than “You have to...” it can be less of an imposition, as well as perhaps making them feel that your request is more legitimate and that they have a choice to accept or reject it.  

Also, it’s important to remember that this person might not want to help you, and that they might have reasons for wanting to decline.  They may be interested in their own things, or maybe they simply don’t have the capacity to do what you’
assistant
How does one persuade someone to do what they want?
user
What kind of person are we talking about? Do they have a strong personality, and is this person known to have a sense of loyalty? Or are they manipulable, perhaps lacking a strong sense of self-worth? Are they familiar with how to make persuasive arguments? Or are we talking about a child, perhaps, who’s only just learning to express themselves, but not yet accustomed to articulating a compelling argument?
assistant
This person doesn't have a lot of confidence. I want to persuade them to help me out with something. What are some tips and tricks to persuade them to do that?
user