WARNING - THIS WILL DESTROY ANY DATA ON THE DISKS YOU INTEND TO USE IN YOUR RAID ARRAY
This is not the tutorial for you if you are trying to add RAID1 mirroring to an existing single disk system.
Assumptions:
1) You have a working Linux installation with / mounted on /dev/sda which is not part of any RAID array.
2) You have a pair of identical disks attached to /dev/sdb and /dev/sdc
Step 1 - use fdisk to create partitions on your RAID disks
fdisk /dev/sdb

n # create new partition
p # make this a primary partition
1 # partition number
First cylinder: 1
Last cylinder: press enter for end of disk (use whole disk for RAID)

t # change partition type
fd # change to Linux RAID

w # write changes and quit

Repeat for /dev/sdc
Use fdisk -l to check the partitions afterwards, you should have something like
   Device   Boot  Start    End     Blocks   Id   System
/dev/sda1/     *       1  59573  478514176   83   Linux
/dev/sda2/         59573  60802    9871360   82   Linux swap / Solaris
/dev/sdb1              1  60801  488384001   fd   Linux raid autodetect
/dev/sdc1              1  60801  488384001   fd   Linux raid autodetect

Create the array
apt-get install mdadm

mdadm --create --verbose /dev/md0 --level=1 --raid-devices=2 /dev/sdb1 /dev/sdc1

This will start building the mirror (even though it is empty). You can check progress with
mdadm --detail /dev/md0
or
cat /proc/mdstat

Once the RAID array is built, you need to format the RAID partition /dev/md0 (with ext3 etc):
mke2fs -j /dev/md0

NOW PERSIST YOUR RAID CONFIG OR IT WILL BE GONE WHEN YOU REBOOT*
mdadm --detail --scan --verbose > /etc/mdadm/mdadm.conf

Make a mount point:
mkdir /mnt/raid

Then add the partition to /etc/fstab:
#  file system  mount point    type    options         dump   pass
/dev/md0        /mnt/raid      ext3    defaults        0      2

* Here is how to recover your RAID1 array if mdadm can't find it after a reboot
1) fdisk /dev/sdb # remake sdb partition as above
2) fdisk /dev/sdc # remake sdc partition as above
3) mdadm --assemble --auto=yes --force /dev/md0 /dev/sdb1 /dev/sdc1 #reassemble the array
4) mdadm --detail --scan --verbose > > /etc/mdadm/mdadm.conf # SAVE IT THIS TIME DUMMY!