If you are less comfortable with command line: clonezilla.
Otherwise: dd
Clone the drive:
Use dd to clone the 1 TB drive to the 2 TB drive. The basic command is:
dd if=/dev/sda of=/dev/sdb bs=1M
Resize the filesystem:
After cloning, you'll need to resize the filesystem to take advantage of the extra space on the 2 TB drive. You can use a tool like resize2fs (for ext2/3/4 filesystems) or xfs_growfs (for XFS filesystems) to do this.