How to make sure only one instance of a bash script runs?

Almost like nsg's answer: use a lock directory. Directory creation is atomic under linux and unix and *BSD and a lot of other OSes.

if mkdir $LOCKDIR
then
    # Do important, exclusive stuff
    if rmdir $LOCKDIR
    then
        echo "Victory is mine"
    else
        echo "Could not remove lock dir" >&2
    fi
else
    # Handle error condition
    ...
fi

You can put the PID of the locking sh into a file in the lock directory for debugging purposes, but don't fall into the trap of thinking you can check that PID to see if the locking process still executes. Lots of race conditions lie down that path.

To add to Bruce Ediger's answer, and inspired by this answer, you should also add more smarts to the cleanup to guard against script termination:

#Remove the lock directory
function cleanup {
    if rmdir $LOCKDIR; then
        echo "Finished"
    else
        echo "Failed to remove lock directory '$LOCKDIR'"
        exit 1
    fi
}

if mkdir $LOCKDIR; then
    #Ensure that if we "grabbed a lock", we release it
    #Works for SIGTERM and SIGINT(Ctrl-C)
    trap "cleanup" EXIT

    echo "Acquired lock, running"

    # Processing starts here
else
    echo "Could not create lock directory '$LOCKDIR'"
    exit 1
fi

One other way to make sure a single instance of bash script runs:

#!/bin/bash

# Check if another instance of script is running
pidof -o %PPID -x $0 >/dev/null && echo "ERROR: Script $0 already running" && exit 1

...

pidof -o %PPID -x $0 gets the PID of the existing script if its already running or exits with error code 1 if no other script is running