The easist way to do it is to:
1. fdisk to make the partitions on the new disk
2. create the filesystem (different tools for diferent fs)
3. mount the disk in some temporary space eg /mnt/home2
4. copy all the data over from /home to /mnt/home2 ensuring that you
maintain file permissions
5. edit f
Yes you can mount your new drive into /home.
Any data already in that directoty will not be accessable until you
unmount the new drive.
If you move the entire /home directory to say /hometemp and then mount
your new drive to /home, you can then copy all the data from /hometemp
to the new drive an