On most systems, you can type C-x * to start the Calculator.
The key sequence C-x * is bound to the command
which can be rebound if convenient (see Customizing Calc).
When you press C-x *, Emacs waits for you to press a second key to complete the command. In this case, you will follow C-x * with a letter (upper- or lower-case, it doesn't matter for C-x *) that says which Calc interface you want to use.
To get Calc's standard interface, type C-x * c. To get Keypad mode, type C-x * k. Type C-x * ? to get a brief list of the available options, and type a second ? to get a complete list.
To ease typing, C-x * * also works to start Calc. It starts the same interface (either C-x * c or C-x * k) that you last used, selecting the C-x * c interface by default.
If C-x * 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.
The same commands (like C-x * c or C-x * *) that start the Calculator also turn it off if it is already on.