Here's a 'Hello World' Linux kernel module example. The C code here is derived from 'The Linux Documentation Project' www site, which also contains more details about getting started writing your own modules.

Note: I still need to read up on what exactly a 'tainted' kernel is.

#include <linux/module.h>
#include <linux/kernel.h>

/* If MODULE_LICENSE is not specified you will see
 * messages like the below in '/var/log/messages':
 *
 * Sep 25 21:35:59 hostname kernel: [722119.034840] Disabling lock debugging due to kernel taint
 * Sep 25 21:35:59 hostname kernel: [722119.034844] LinuxKernelModuleExample: module license 'unspecified' taints kernel.
 */
MODULE_LICENSE("gpl");

int init_module(void) {
	/* Log message with log level 'KERN_INFO'.
	 * Message will display in '/var/log/messages'
	 */
	printk(KERN_INFO "init_module\n");
	return 0;
}

void cleanup_module(void) {
	/* Log message with log level 'KERN_INFO'.
	 * Message will display in '/var/log/messages'
	 */
	printk(KERN_INFO "cleanup_module\n");
}

obj-m += LinuxKernelModuleExample.o

all:
	make -C /lib/modules/$(shell uname -r)/build M=$(PWD) modules

clean:
	make -C /lib/modules/$(shell uname -r)/build M=$(PWD) clean

#
#Need to run all of the below as root
#
info:
	modinfo LinuxKernelModuleExample.ko
#
# Copy the new module to /lib/modules/`uname -r` because
# modprobe looks for modules by default here.
#
# Also modprobe expects that modules.dep exists in this folder as well.
#
install:
	cp ./LinuxKernelModuleExample.ko /lib/modules/`uname -r`
	depmod /lib/modules/`uname -r`/LinuxKernelModuleExample.ko
	modprobe -a LinuxKernelModuleExample
#
# See if the kernel module is installed, amd dump the tail of the log
#	
lsmod:
	ls | grep LinuxKernelModuleExample
	tail /var/log/messages

#
# Remove the kernel module	
#
remove:
	modprobe -r LinuxKernelModuleExample
	rm -f /lib/modules/`uname -r`/LinuxKernelModuleExample.ko 
	ls /lib/modules/`uname -r` 

#
# Test the module
#
test: install lsmod remove