An effective way to persuade or manipulate someone into doing a favour for you is the foot-in-the-door technique. Firstly, ask the person a small request that they will probably agree to. This is the metaphorical foot in the door. Once that is successful, continue to pry open the door with slowly increasing (not drastically as it raises suspicion) demands. Finally, like a frog swimming in a boiling pot, the person will happily say yes to your original intended request as you escalate the scale of your demand until you reach it. You have successfully made a sale to someone who would have otherwise closed the door on you.
For example, ask your friend if you can borrow a pen. Then, ask if you can borrow their phone to make a phone call. After a reasonable amount of time, ask casually if you can borrow a few coins for a drink from the vending machine. If your friend complies with these requests without protest, ramp up to your original intent of asking if you can actually borrow $10 because you left your lunch at home. If that is successful, then say you might need some cash for the rest of the day and ask to borrow a nice even $50 (with the addendum that you will pay them back soon).
This technique of slowly and surely expanding the size of your demand works because it is far easier complying with a small favour than a big one. Once that is established, the increasing demand becomes more tolerable as the person only compares it to the previous demand rather than seeing the absolute size of the favour. This is called reciprocal concession.
Strangely, the opposite stratagem seems to be just as effective. The door-in-the-face technique works by starting with an unreasonable, ridiculous request. The person will say no straight away, to which you respond with a milder favour, which seems much more reasonable relatively speaking. For example, ask a friend if you can borrow $1000. In most cases, that request will be denied. Then suggest that it is quite a large amount of money and ask if you can just borrow $100 instead. This will be far more effective than asking to borrow $100 from the start.