In general, the courts don’t “determine the current standards” at all. If you’ll remember, the constitution requires that a court only act on a real “case or controversy.” So if someone challenges twenty years at hard labor for littering as disproportionate under the Eighth Amendment, the courts look at that one claim, and adjudge whether it is “cruel or unusual” (note that disproportionateness is an element of whether it is “cruel” – the case of the male teen charged with statutory sodomy for giving a younger teen (also male) a blowjob and sentenced to 17 years prison when the maximum sentence for a heterosexual statutory sex crime involving youths of their ages was 15 months, is a pretty typical case of disproportionateness).
As to where they get their ideas from: political columnists, editorial writers, and writers of letters to the editor, have been staples of newspapers since the earliest days of America. Today, blogs, message boards, and other Internet-based publicizing of opinion can be added to that. In the past, the writing and circulation of pamphlets and fliers, the making and posting of posters, etc., were common means of expressing political views publicly.
In an argument for cruelness or disproportionateness, the attorney for the convicted will make a case using such evidence as he cares to present. Testimony on the effects of a given sentence by a penologist, the editorial page of the New York Times, a comment by Molly Ivins or George Will, amicus curiae briefs from “Citizens Against Ridiculous Excess in Sentencing”[CARES]), whatever. The attorney representing the state (usually on the staff of the state attorney general) will counterargue that the sentence is appropriate for the circumstances of the crime and offender.
In arguments relating to unusualness and again disproportionatness, the attorney will display evidence relating to what sentence was imposed in similar offenses elsewhere – as will the state’s attorney, both sides cherry-picking the material that best makes their case.
I get the impression that you feel that judges pull their opinions out of thin air or fundamental areas of their anatomy, What the…!!! – generally they are founded on legal principles, including the fact that words have meanings and that those meanings change slowly but inexorably with time.
If our standards as a people today about what sorts of punishment are cruel and unusual are somewhat different than they were when Lincoln was reading law, that reflects an element of our social contract. Our entry into Iraq in 2003, for example, would have rendered the entire Congress of 1940 or 1950 totally aghast, liberal and conservative alike. Where a law uses words that are not “legal terms of art,” a court is obliged to construe them in the way that the public understands them.