That is a very open-ended question. A dependency occurs when one (or more) processes cannot begin, or be executed until a certain state (or condition) exists. For example, you cannot start your car until the key is in the ignition. Starting the car (process) can not occur until the key is in the ignition (state/condition).
The Project Manager needs some familiarity with and understanding of the nature and purpose of the project in order to define dependencies. The more familiarity the PM has, the easier it will be for him/her to determine what the dependencies are.
In MS project or most PM tools for that, have dependancies as FS, SF, FF, SS, which means you cannot link a task to another task if that task has not met the rules, so this gives us:
FS - Finish Start e.g. you cannot start the task until the task it i linked to or dependent upon is completed, you can start the car untill the keys are in the ignition and you cannot drive off until the car is running and in gear.
SF - Start - Finish e.g. this is least used, well on my projects anyway. This is a task a cannot start until task b is finished, so if you hd a resource and he was working on task a and task b
FF - Finish - Finish e.g. a task cannot finish until another task is still running, you cannot sign off on testing until the testing is complete
SS - Start - Start e.g. you cannot start task a until task b is ready to start, so you cannot install the hardware in the rack until the rack is installed
and then you can add to dependancies by adding delays of days or hours
This is a good place to start: http://office.microsoft.com/en-us/project/HA010211721033.aspx