One of the hardest things I've found about weeding is knowing that funding to replace out of date books tends to be minimal at best.
Because of that, I generally do a light weeding rotation that takes a year or two to complete to get through the entire library--it's naturally taking less and less time to go through as more books are pulled--and choose one or two sections a year to do a heavy weed on. This section is then replaced as much as possible with that year's funding.
Books you will probably need to get rid of: All your computer books, old almanacs and other references, dinosaur books that mention brontosaurs, books about extinct animals that weren't extinct when the books were written, most of your health section, most of your music section, books on space exploration that don't mention the shuttle or the space station, and a positively terrifying amount of your 900's. Any biographies of deceased people that meet the "I've (the librarian) never heard of them" criterion are fair game.
Above all, don't be afraid to be ruthless: your library, if it is like mine was, could probably lose at least a third or more of its books and be all the better for it.
Oh, and one hint: when weeding the 800s and the reference section, I recommend wearing a dust mask. (One could plant potatoes on some of those reference books.)