On most systems, you can type M-# to start the Calculator. The notation M-# is short for Meta-#. On most keyboards this means holding down the Meta (or Alt) and Shift keys while typing 3.
Once again, if you don't have a Meta key on your keyboard you can type ESC first, then #, to accomplish the same thing. If you don't even have an ESC key, you can fake it by holding down Control or CTRL while typing a left square bracket (that's C-[ in Emacs notation).
M-# is a prefix key; when you press it, Emacs waits for you to press a second key to complete the command. In this case, you will follow M-# with a letter (upper- or lower-case, it doesn't matter for M-#) that says which Calc interface you want to use.
To get Calc's standard interface, type M-# c. To get Keypad Mode, type M-# k. Type M-# ? to get a brief list of the available options, and type a second ? to get a complete list.
To ease typing, M-# M-# (or M-# # if that's easier) also works to start Calc. It starts the same interface (either M-# c or M-# k) that you last used, selecting the M-# c interface by default. (If your installation has a special function key set up to act like M-#, hitting that function key twice is just like hitting M-# M-#.)
If M-# doesn't work for you, you can always type explicit commands like M-x calc (for the standard user interface) or M-x calc-keypad (for Keypad Mode). First type M-x (that's Meta with the letter x), then, at the prompt, type the full command (like calc-keypad) and press Return.
If you type M-x calc and Emacs still doesn't recognize the command (it will say `[No match]' when you try to press RET), then Calc has not been properly installed.
The same commands (like M-# c or M-# M-#) that start the Calculator also turn it off if it is already on.