I read and watch social history, and they use letters to newspapers as a source. How do you tell it isn’t from a crank which is just printed to make everyone laugh, and elicit response letters?
If you're doing any kind of history, one of the things you have to consider is how you treat your sources and what you know about them, and also to make sure you've read enough into whatever you're studying to understand its uses and limitations. Letters to a newspaper editor are a primary source -- that is, they are something like letters sent among persons, or diaries, or other pieces of writing that people do personally. Letters to an editor are different from edited articles in a newspaper (although many early newspapers were mostly letters that editors published).
To illustrate this, imagine that I'm a newspaper reporter (which I once was) and I go out to a city council meeting. I would read the agenda, listen to the discussion, hopefully talk to citizens and council members about decisions that were made, and then write a story that summarizes or interprets what happened. Another person or two will read this, edit it, potentially make changes, write a headline and slap it on a page -- so that's a secondary account of the meeting; a verbatim transcript would be a primary source (and horrendously boring).
Going back to primary sources for a minute: your question is "how do we know that letters are accurate" (I'm paraphrasing). And the answer is that we can't know that letters reflect the view of those who wrote them. This is a problem with any primary source -- the Book of Revelation reads like it was written by someone off their mind on a hallucinogen, which probably means it was written by someone off their mind on a hallucinogen, but we can't know that for sure!
But if we read a lot of letters in newspapers over a large volume of time, we can get a good feeling for the aggregate public sentiment over time, or local variants of it from what we've been reading. We need to understand that for newspapers in particular, what the editor chooses to print may or may not reflect the general consensus of things -- in the olden days when I was an editor, we would put crank letters into the circular file (mostly, the really good ones we'd put up on the office bulletin board). In the days before some wunderkind at Poynter decided it would be a good idea to put a comment widget on every story on the Internet, what people were able to say in a publication was curated by editors. (Most publications, before journalism went completely to hell in the mid-noughties, made a good-faith effort to publish views from across the political spectrum, but from my experience we would still pitch things about worldwide Jewish conspiracies, or other outwardly racist stuff, or whatever.)
OK, so I started rambling. Let's focus back on the question: Again, we can't be sure that everything a newspaper published was the exact view of the person who wrote it. My grandmother was a frequent complainer to the Kansas City Times and the Kansas City Star, and they had a policy that they'd only publish so many letters from a given person per month, so she made up pseudonyms to try to get letters in. (It didn't occur to her that they'd read the return address label.) Did she slip a few past the goalie? Sure, but it's the job of the historian to read, understand, and contextualize sources to see if you can understand what "public opinion" was in the past, and letters to the editor are no worse than any other primary source for that. When I studied attitudes towards objectivity in newspapers during Reconstruction (my master's thesis), I got a very good feel for which editors were writing what under which pseudonym based on their writing style.
For further reading, I would recommend these older Monday Methods threads: