The cursor (the little image on the screen that moves in relation to your physical movements when manipulating the mouse's planar orientation against a flat surface) tells you a lot about what it's on-top of.
For the large part, a single click is all that's required, unless opening files.
The default arrow means if you click (depress the large button on the left side of the mouse) once, the thing behind the cursor will be selected. In geek-speak, we say the object has focus.
If you double-click (depress the left mouse button twice in rapid succession), you will activate the object's default action. With files, this is generally "Open".
Messages, options and menus (like "OK" and "Save") only require a single click.
When the cursor is a hand with a pointing finger, it signifies that you are over an interactive object, such as a hyperlink. These only require a single click. It's rare that double-clicking is required when browsing the Internet.
When the cursor is an I-bar, it signifies that the cursor is over a text field.
Click once to activate that field and begin typing to enter text.
If you want to know what actions are available or intend to select an action other than the default one, right-click. This will invoke what's called a "Context menu". It is a list of what you can do with that object. Left-click to select the option you require, or press "Esc" on the keyboard or click somewhere off the list to cancel it.
When the cursor is something rotating or spinning, it generally means the computer is working on something. Patience is best employed here.
Finally, there are other cursors when you use special programs like photo editors or games, that indicate which tool you currently have selected.
Interacting with a computer is a lot like having a conversation. You give a command and wait for a response.