Politicians are likely to dismiss the excellent 'Twenty tips for interpreting scientific claims' after a few lines, simply because these tips are not geared to their everyday needs (W. J. Sutherland et al. Nature 503, 335–337; 2013). I have some other suggestions for them.
Science is open-minded, but not empty-headed. Just because there is no definitive answer to a problem does not mean that any alternative is equally good. Not all evidence may point in one direction. Trust the weight of evidence.
Avoid 'false balance' on scientific issues. There will always be naysayers. That is fine in politics, in which everyone is entitled to their opinions, but not in science, in which one produces the evidence or holds one's peace.
Science is not decided by vote. Most scientists have little expertise outside their own fields. Let people who really understand the issues help you to evaluate the evidence.
Enlist the best advice on scientific issues. Do not rely on 'independent scholars' and think-tank policy wonks for advice and referrals. Every country has academies of science and excellent universities to consult.
Steer clear of science that has not been peer reviewed. Conscientious analysis by our peers makes science work. It does not ensure certitude, but it beats the alternative.
Championing good science makes you look good. Know-nothings and anti-intellectuals will try to undermine your principled support of some scientific issues. Turn their ignorance against them by showing the consequences of following their path.
Non-scientists could also consult undsci.berkeley.edu for an introduction to how science is done.