A foolish consistency is the hobgoblin of little minds.
—Ralph Waldo Emerson
That's it, basically. If you have something important to influence about, learn everything you can about it. Read everything you can find, talk to everyone who knows more about it than you do. Don't limit yourself by looking only for support or justification of your point of view. Get familiar with all the counterarguments and all the potential threats that are related to your idea—all the needs and fears that might arise for someone who actually had to agree to take action on it. Put yourself in the place of the person you wish to influence and make an educated guess about the specific issues that your request or offer will raise for her or him. Think yourself into the mind of someone who would be unalterably opposed to doing what you want done and then see what it would take to change your mind, even to warm up to the idea just a little.
Develop a list of benefits and costs for taking action—not just for you (although that will be useful), but for the person or group you hope to influence. Do a risk analysis. Identify what could go wrong and how such problems could be prevented or mitigated. Be sure to do this from your target person's point of view. Think about the risks of not taking action at all.
Anything you can do to stimulate dissatisfaction with the status quo may help move your idea forward. Some ways to do that include