I'm not a climate scientist and only got into it to win an Internet Argument. It was very important, at the time. ;-)
Basically, I'd worked with modeling large data sets in a chaotic system (traffic) and knew that 'adjusting the data' was legitimate. This was when people were complaining about the scientists changing the data they used in their models.
So, I started poking. I spent about two years poking at it. I also learned that the rumors seemed to be untrue. I was able to email and get unadjusted data - even without credentials. I say 'seemed' because this was after the email disclosures.
If you just want a copy of a paper and you don't feel like paying for it or hitting up your local university library, you can even just email one of the authors. I did that a couple of times and have had nothing but cooperation.
If you search the title or visit the author's homepage you can sometimes find a copy hosted, and these days there is of course sci-hub.
I do still pay passing attention but my quasi-scholastic approach has settled down.
One benefit of contacting them directly is you can often get copies of more than just the paper. I've had them send me zipped copies of their research and, in one case, even sent me a couple of DVDs full of stuff.
On a whole, the community was very approachable and I simply explained what I was doing and why. There weren't any negative responses and I was clear that I'm a mathematician and not a climate scientist. It was very unlike how I'd been led to believe, as far as uncooperative responses.