'Préconiser' is more formal than 'conseiller'. You may read it in books and some (usually well-written) press articles. My teachers use 'préconiser' almost every day to let us know which is their favourite method (e.g. 'Dans ce cas, je préconise l'utilisation de ..."), and yes they do speak rather formally in general. Another difference is the structure following the verb: 'préconiser quelque chose' vs 'conseiller quelque chose (à quelqu'un)'. 'Préconiser' is never followed by an indirect object. You can also use 'recommander' (same structure as 'conseiller') instead of 'préconiser' (which I think is a better synonym in most cases). Hyoshin has a very good point: if you speak too formally (when you're usually not supposed to), most people would assume you're just showing off. If people around you don't seem to use 'préconiser', 'recommander' might be a good alternative. You can find several examples of 'préconiser' being (well) used here: http://www.linternaute.com/dictionnaire/fr/definition/preconiser/#evenement

"Préconiser" is a little stronger than "conseiller". And YES a lot of people DO use it and they do not have a broom up...., It is not , because some people don't use a particular word that they have to insult those who do. It is just a question of richness of a language.

The answer is simple: never. I've literally never ever heard someone use 'préconiser' in my life. Must be one of those words people use to make themselves sound smart but whatever, they just sound like they have a broom up their ass. :P Just use natural words that everyone could understand, that's much more intelligent. :D

It is a bit more formal, stronger and it often implies that the person (who "préconise") is an expert or an authority figure. If you're ill, your friend will say "je te conseille de dormir", but a doctor might say "je vous préconise du repos". If you write an essay, you might also conclude by saying "je préconise de faire cela" to solve a problem rather than "je conseille", but again, you're in a kind of authority position giving recommendations.