Actions speak louder than words. The best way of influencing those around you is when they can see that you are donating time and money to a cause you believe in passionately – and that doing so is making the world a better place.
If you can tie in your own personal story of exploration of these ideas into the narrative. How did you come across EA ideas? What inspired you? What things do you do? What changed you? Etc.
If you cannot provide your own story a story of a friend will work too. Eg: “my friend K was really nervous about giving 10% but then . . .”
For example many people want to make the world better. The EA community can help them better achieve this goal. It can also help with many other common goals: provide friends / meaning / volunteering opportunities / happiness / etc.
Agree with the person you are talking to as much as you honestly can. If they express a belief agree it is a valid belief and then work within that framework. Eg: “yes that makes sense as a reason to prioritise our community first, but for me personally when I realise how much good even tiny amount of donations to the developing world can . . . .”
Do not say “no you are wrong” unless it is a very clear factual inaccuracy where you are sure you have strong evidence that will make them update their views. Even then try to soften it with a phrase like “that is a common myth; the current consensus is . . .”
It can be useful to begin introducing EA with a really basic uncontroversial definition that no one can reasonably disagree with, something like: "Effective Altruism is applying evidence, reason and rationality to the goal of making the world a better place."
How exactly we should present stuff needs to be decided on a case by case basis. Stop and think: 'here is a new person, how best to present EA ideas to them, what do I know about them'.
Ideally try to avoid telling people that they are obliged to do any particular action. Especially try not to tell people that what they are currently doing is bad.
More generally you should shy away from subjective claims where you are unsure if the other person will agree with you. Such as “x is immoral” or “rap is the best music” etc.
All the tips here are focused on talking about EA to people. Being a good communicator in general would also help. Perhaps go do some general research into how to be a good speaker.
An example way of explaining effective altruism to someone for the first time: