Alerts come when the awareness meter above an enemy's head turns red and they start shooting at you. As for not killing anyone, learn to blink passed enemies, utilize your sleep bolts for your crossbow ( + to the top left), you'll know they're sleep darts because they're green. Also be sure you use knockout takedowns by holding when you're behind an enemy. One last tip would be to hold while you're knocking them out so you catch them as they collapse, otherwise they'll fall to the ground and possibly alert nearby enemies.
Whenever you finish a mission, it shows two boxes at the bottom for killing or alerting people. You must complete the entire game with both of those boxes checked for every mission. You cannot replay them later, it must be in one playthrough. If you messed up you must replay the level (do not exit the game and try mission select, it does not work). It's obviously best to play this on easy. Some people prefer to be able to upgrade and use powers, while most people wish to stack this, Clean Hands, and Mostly Flesh and Steel together. If you are using a rune you are voiding your achievement. So do not upgrade Blink if trying to stack these achievements.
Check here for tips on how to get Clean Hands, Mostly flesh and Steel, and Ghost all in one playthrough.