The implementation of chests, locks, and traps in Din's Curse is the topic of Steven Peeler's most recent blog entry over at the game's official website.
When you get close to a chest, you get a good bit of information about it- whether or not it's locked, your chance to pick the lock, what kind of trap you think it has, what's your chance of being right about the trap, and your chance to disarm it. That sounds like a lot, but it really boils down to is it locked and/or trapped.
First off, what if the chest is locked? Well if you have a skeleton key, you are good to go. Just use the door, you will use up one key, and the door will open (it might set off a trap though). However, skeleton keys are fairly rare and expensive (at least to new characters). Rogues or a hybrid character with the thief specialty has a pick locks skill. Picking a lock takes a bit of time and uses up some of your mana. The chance that you are actually successful depends on your skill level compared to the level of the lock.