I have not seen the cinema trailer,so I don't get the 'ledge' reference either.
But I love this movie.
If you have seen a few Coen Brothers movies you should hopefully have some idea of the type of humour you are in for. It's not laugh-out-loud/gross-out/sledgehammer, obvious style humour. It's subtle stuff, and the humour is to be found primarily in the dialogue and the characterisations.
Jeff Bridges just...is...the Dude. It's a role that he looks like he was born to play his whole life. He's a kind of stoner, a waster, though one given to occasional bouts of philosophy, with his own unique world view.
The shot of him walking around a supermarket in just shorts, t shirt, dressing gown and slippers drinking from milk cartons kind of sums him up...he lives his life on his own terms, does not bother anyone and does not really care what people think of him.
For reasons too complex to go into, he gets mistaken for another person of the same name (a rich businessman), and suddenly has all sorts of strange people after him, and also gets roped into helping the 'other' Lebowski retrieve his kidnapped wife from a bunch of nihilist nutters.
It's one of those movies that creates it's own mood and reality. There are sequences and lines of dialogue that I find hilarious, but to quote them out of context just would not work...they are not jokes, they are not wittiscisms in the usual way...but within the confines of the movie they can reduce you to tears of laughter, that's if you are able to go along with the concept and accept the movies sense of reality.
I have to say, as much as I like Bridges performance as The Dude, I also love John Goodman's uptight, embittered vietnam vet...pulling a gun at a bowling alley because he thinks someone has incurred a minor rule infringement...'I didn't watch my buddies die face down in the mud in 'Nam so that people could break the rules!'.