Ways to increase your odds of persuading people, robots, and mutants through speech in the Fallout universe:

- Wear sexy clothing
- Drink the right booze
- Consume other questionable substances
- Wear the right hat
- Wear ridiculous glasses
- Locate a bobblehead
- Be given, but not necessarily do anything with, a bear necklace
- Intensely train your charisma
- Read magazines about meeting people
- Find and consume copies of a particular book 
- Read a book intended for infants
- Surgically implant simulated empathy into your skull

Note that context makes absolutely no difference as to whether any of the above will improve your chances. All of them will help regardless of who you're talking to or what you're trying to persuade them about.