There are two ways of doing it: by making a raw copy of one media to another, or by re-creating partitions, and copying the contents.

Regardless of the method, switch to single-user runlevel, make sure no user-space processes are running beside init and the shell and remount the root filesystem read-only

mount / -o remount,ro

Raw copy

Contents copying

Partition the new media (assuming it is on /dev/hda, and hda1 will be the root partition)

sudo fdisk /dev/hda

format the root filesystem. Use ext2 if it is a solid state device

mkfs -t ext3 /dev/hda1

Moun the new partition and, assuming it is mounted on /mnt/hda1, copy the contents to the new partition

copy -ar /bin /boot  /etc  /home  /initrd  /initrd.img  /lib  /lost+found  /opt  /root  /sbin  /selinux /srv /usr  /var  /vmlinuz /dev /mnt/hda1

mkdir /mnt/hda1/proc  /mnt/hda1/sys

grub
> root (hdX,0)
> setup (hdx)

if swap partition doesnt mount properly, try

mkswap /dev//hdaX
swapon /dev/hdaX