How does a Linux/Unix Bash script know its own PID?

The variable '$$' contains the PID.

use $BASHPID or $$

See the [manual][1] for more information, including differences between the two.

TL;DRTFM

• $$ Expands to the process ID of the shell.
  • In a () subshell, it expands to the process ID of the invoking shell, not the subshell.
• $BASHPID Expands to the process ID of the current Bash process (new to bash 4).
  • In a () subshell, it expands to the process ID of the subshell [1]: http://www.gnu.org/software/bash/manual/bashref.html#Bash-Variables

In addition to the example given in the Advanced Bash Scripting Guide referenced by Jefromi, these examples show how pipes create subshells:

$ echo $$ $BASHPID | cat -
11656 31528
$ echo $$ $BASHPID
11656 11656
$ echo $$ | while read line; do echo $line $$ $BASHPID; done
11656 11656 31497
$ while read line; do echo $line $$ $BASHPID; done <<< $$
11656 11656 11656