In a discussion on the Old Felicifia, Gaverick suggested that fundraising/advertising were massively underfunded by activist organizations. I would hypothesize at least two reasons: (1) Organizations don't want to be seen as wasting precious donor money on advertising, and doing so reduces the fraction of money they spend on program costs. (2) Activists have a general aversion to advertising because it feels like something that is mostly done with commercial intent.
There's another good reason, which is that (3) if your ads will principally pull money or followers away from other groups doing roughly the same thing as you are, then the advertising is zero-sum.
Both (1) and (3) are important caveats to keep in mind. However, those of us on this forum generally think that we do know of some causes which are (much) more cost-effective than others, so even if we pull away supporters from other things, there's still a big net gain.
It is remarkably easy to create an ad campaign, and you don't even need the sponsorship of an organization. Anyone can create a simple ad linking to a web page with less than an hour of setup. You might want to spend a few extra hours learning about the theory of web advertising, reading policies and best practices, etc., but the core steps of creating the ad are just a few pages long.
For example, take a look at Facebook's ads page and click "Create An Ad". I created a fake ad for my essay on wild-animal suffering just to see the process. You can target toward specific countries, ages, genders, Facebook interest categories, languages, etc. I think it's best to aim at young people (say, 13-25 years old) because (a) young minds are most open to new things and (b) they have the longest time ahead of them to donate, not eat meat, choose optimal careers, and participate in our projects.
The costs are pretty decent. For United States, the suggested bid that Facebook gave me was $0.54 per click. $0.44 for UK, $0.22 for India, $0.19 for China, $0.12 for Mexico, $0.12 for Sri Lanka, etc.
I wonder if 80,000 Hours, Global Happiness Organization, Giving What We Can, etc. should try a few online ads, at least as a pilot effort to see how they work. (I may eventually try some for my website, though I'd prefer to wait until later so that I'll be able to handle the increased traffic load and perhaps improve the aesthetics of the pages.)
If you want to use your ads for scientific purposes, you could create several different flavors of descriptions + pictures and see which ones produce highest conversion rates. In fact, you could test the appeal of almost any slogan or meme in this way -- your ads could be your own, personal public-opinion-polling system -- although it could get expensive if only used for this purpose.