If no target or object is given, you will look around your current environment. If you specify a target (which could be another player, an NPC, an object in the room, or something mentioned in the description of the room), you will examine that target more closely.
This command is globally aliased to l, so instead of typing look with any of these syntaxes, you only need to use the letter l.
In all examples, < > surrounds variables. You shouldn't type the < >.
look <target or object>
look at <target or object>
look <target or object> here - this command is the same as the above but it will only check for the target or object in your location. This is useful in cases like when you have a symbol in your possession, and want to look at a symbol that is in the room.
look at <something> on <object> - look at some specific part of an object that is either in the room or in your possession. Also look at items another player is displaying (help displaying)
look <object> # - for multiple objects that share an id you can use this to look at ones other than the the first (example: look sword 3)
See also: smell, taste, touch, feel, listen, glance, displaying