The simplest answer is to hide those things that cannot reasonably be known by the character, or figured out routinely by the player, and give such details as are necessary.
AC is a tricky one. Some details can be figured out easily (the guard is wearing chain mail, so his AC is probably around X), but sometimes you'll want to lob a few surprises at people (like the guy with magic armor, or a Ring of Protection, which are each a little less obvious). My way around this was simple: give the players the combat tables, so that when they roll and add all their modifiers they can say "I hit AC X", and then you can tell them whether or not that was good enough. This way, you can maintain a little bit of mystery if need be (Was that high roll needed to hit? Did I just miss, or was I way off?) and also let you insert a little color in the results ("The guard barely manages to get his shield up to deflect your blow, you almost had him!", or "The creature easily dodges your attack, and you hear a hissing laugh as he prepares to strike." for instance.)
Other bits of information should definitely NOT be revealed easily...my favorite example being the check for traps. One of my favorite phrases as a GM has long been "You don't find any traps...", which could mean anything from "you blew it" to "there aren't any", and is a lovely little paranoia-inducer, though it requires that you use some method of obscuring the value of dice rolls (for example, randomly determining whether a high roll or a low one will be successful, which keeps the players from automatically knowing...some groups really dislike this sort of thing, however.)
The trick here, though, is remembering the difference between "information" and "mechanics". Mechanics don't, by themselves, need to remain hidden from the players (and characters). Players should have a reasonable expectation of knowing how the game and the world works, at the relatively simple level of mechanics, so that they can make plans and devise tactics. What they shouldn't have is perfect information about the situation (without having earned it) that will allow them to devise "perfect" plans and tactics. Gaining information is part of the game, and success or failure at it should have an impact upon the outcome of an adventure in some way.