A few tips:
- if possible, use a usb3 interface and harddisk. Modern laptops usually have that. Usb3 is much faster than usb2.
- make just one full system backup and then start making incremental backups of your data (usually your user's directory). Incremental backups only store delta's which mean it only stores the differences with the last backup, is much quicker.
- use software that can make "snapshots"
- make your backup on a least 2 external disks and store them in different places.
- as Dave said, don't touch your computer during backup and turn off internet connection. Close all running programs.
Good backups take time.
I myself use a NAS ( network attached storage ) to make dayly incremental backups which per day don't take much time. As the NAS is in my network, so I can always do the backup when I please, even over the internet when I'm abroad every week, the NAS is manually backupped on an external harddisk which is stored at my work.