With education. And with a factual description of the problem and the available solutions. With outright rejection of denialism. With rejection of feelgood non-activism like plastic straw bans and tree-planting measures. Don't get me wrong, those things are good and a step in the right direction, but they're far too little far too late compared to what must be done, and so they're inactivism that wastes public energy on measures that don't move the needle in addressing the problem.
This doesn't even fly with 'enlightened' crowds like HN out of the box because they'll tend to kneejerk about things like nuclear power + electrochemical CO2 sequestration despite it being the only realistic option to dig ourselves out of the hole we're in. Worth noting that the mainstream crowds in China/Russia are a lot more pragmatic about this than AU/UK/US.
I'm pretty sure this comment is going to be downvoted just for mentioning it, but I'll drop it anyway to genuinely answer your question. A lot of the folk I know in the field have basically given up hope to avert this and become gloom and doom in the last 5 years, including people you would've seen on TV at the Paris Accords. They are probably right. It's pretty depressing info to handle. I'm sorry I don't have a better answer, but people much smarter than me don't seem to have one either.
tl;dr: Like Bill Gates puts it, misdirected climate activists are actually a bigger problem than climate deniers at this point.
Is there a network of climate change science think tanks dedicated to framing the climate change debate in a way that benefits the climate change community?
Do climate scientists run social media "consultancies" to make a pro-climate change case on the major social platforms and smaller forums?
If any of the above happen - questionable, but let's pretend - they're at tiny outlier scale compared to the organised lies, smears, denial and general FUD put out by the denialist corporates.
You say you've been warning about catastrophic climate change since the early 00s. What in your opinion would be the best way to counter climate denial PR?
Because clearly simply informing the public of the facts isn't going to do anything against the noise being made by the denialist side.