Depending on the keyboard used, the keystrokes may vary.
Screenshot of entire screen
If you are using Apple Keyboard the combination is Command+Shift+3 keys together pressed and released. Once the keys are released, the screenshot will be stored in the desktop itself.
If you are using Conventional Keyboard for Macs (Ex: For Mac mini, etc), the key combination is
(See the screenshot below)
|Screenshot in Mac (OS X)|
Screenshot of a particular Area
To take the screenshot of a particular area, then you can use Command+shift+4 keys pressed and released. Once released, you will get a + symbol with x and y location. Simply drag the area you want to take a screenshot and release it. Thats it!!!. See the screenshot taken using this method.
|screenshot in mac using Command+shift+4|
|Screenshot in mac before taking a Command+shift+4|
Also, there are other methods like storing the image to a clipboard and later can be used inside the document processing applications. Also there is a provision for storing the screenshot files in an user specified location rather than on the Desktop.
If you want to record your screen, Mac OS X has the method using Quick Time player. There may not be any need for desktop recording application, the quick time player will do that. But if you need a complete customization pack, then you may think of any such app.