How do I find out how to do things in Mathematica?

Mathematica comes with an extensive built in help system to assist you in learning how to best use the software. The Help Browser is a complete reference including all 1600 pages of The Mathematica Book and all the supplemental documentation online. A good place to start learning about Mathematica is the Tour of Mathematica found either in the Help Browser, the hardcopy Mathematica book, or on this website.

Assistance for functions

If you are in doubt about a command's name or the arguments it requires, can access a couple of helpers directly from the command line:

Auto Completion

Type the first couple of letters of the command name and press Control-k.  Mathematica will show you a pop-up list of possible completions. 
Try it by clicking the word Plot in the following cell and pressing Control-k. You might have to wait a couple of seconds for the kernel to start up.

Plot

This even works for your own functions and variables.

Function Templates

If you want to see a template of the command and its optional parameters, simply press Control-Shift-k and Mathematica will provide a template. 
Try it by moving the cursor behind Plot3D and pressing Control-Shift-k.

Plot3D

You should see the following line.

Plot3D[f,  {x,  xmin,  xmax},  {y,  ymin,  ymax}]

Palettes

Of course you can always use the input palettes provided in the File ⊳ Palettes submenu. Simply press the correct button and Mathematica will paste a template of the function call into the notebook. You can use the tab key to enter your parameters.  For example, take a look at Basic Calculations.

The Help Browser

The Mathematica Help Browser, a complete, fully interactive, typeset-quality help system, contains all the Mathematica documentation. This includes

  •   The Mathematica Book
  •   Guide to Standard Add-ons
  •   Getting Started with Mathematica
  
The documentation consists entirely of fully indexed Mathematica notebooks, which offer the same high typesetting quality as the printed documentation. Additionally, all the Help Browser notebooks are fully interactive, so you can execute calculations, make changes and copy and paste. Developers and other advanced users can add their own help notebooks and comments. (By default, the Help Browser discards any changes to its contents, but that can be customized.)

To get to the Help Browser, either press shift-F1 or select Help from the Help menu. To look up specific information, type the name of the function you want to look up and press F1 or select Find in Help from the  Help menu.

By  default, the Help Browser only searches the Built-in Functions part of the index. If you do not find the answer you are looking for there, click the Master Index button and repeat the search.

Further information

There are a number of additional resources available for finding out how to do things in Mathematica. Examples are this web site, other Wolfram Research, Inc. websites like the techncial support site, the library pages and MathSource. Also, the Mathematica bookstore contains hundreds of Mathematica related books. If you are interested in getting personalized training or consulting, Wolfram Research maintains a list of accredited training professionals and consultants who have years of experience in the use and teaching of Mathematica. Finally, the newsgroup comp.soft-sys.math.mathematica is a invaluable resource for any questions you might have.

Backward compatibility note ? and ??

You can also get information about built-in functions or packages by typing ?Functionname for basic information or ??Functionname for a more detailed explanation. Generally, however, you will be better of by consulting the Help Browser. If you use only partial function names, you can use the * wildcard.

?Plot

?Plot*

?? Plot