Hey Louise, are you involved in a local group already? I think starting a local group or being an active volunteer in one is one of the best ways to promote EA and build the EA community. It allows you to constantly meet with and help a small group of people learn about EA in a high-fidelity way. 

You can try to find an EA group near you here, or you can join EA Anywhere too. It's very hard to promote EA to lots of people at once, and we don't really want that either, due to the fidelity model of spreading EA ideas.

I did a search on the EA Forum because I know there's been some research done by EAs before on how people give and how to promote effective giving. Here's one written by Jon Behar from The Life You Can Save.

The Life You Can Save has done some work into trying to popularize effective giving to charities helping those in extreme poverty. I think what they do through social proofing (inviting celebrities to read their audiobook) and creating a free e-book are ways to promote EA or effective giving well.

You could also try getting good at journalism or starting a blog about effective altruism. You could also just post on your social media and promote good EA books and content, like Doing Good Better and The Precipice. Hope this answer helps!

There are some studies that touch on questions about promoting effective giving (this is one of the most recent/most directly inspired by EA). 

But the EA community is less focused on particular studies and more interested in evaluating the experience built up by thousands of people having tens of thousands of interactions focused on promoting EA ideas. 

The strategies with the most promising history are generally community-focused, rather than aiming at mass media coverage; people tend to hear about EA through friends or social groups (though there have been a few very successful podcasts).

If you don't already have a major platform (like a big podcast/stream/YouTube channel/etc.), I think you'd be best served by:

1. Finding an EA group near you (as Brian suggested -- see the links in his answer)
2. Trying some promotion within your social circle (for example, with a birthday post)
3. Thinking about unusual resources/skills you might have, and making a follow-up post based on those -- for example, the filmmaker Simon Panrucker asked about applying his skills to EA promotion and got a lot of advice.
   1. That said, most people's specialties don't map as neatly onto promotion as Simon's did -- don't feel bad if nothing comes to mind.