There are plenty of guides explaining how to upgrade /move to a bigger hard drive. There are a lot fewer explaining how to move your working system to a smaller hard drive. Fewer still that actually work easily!
Why would you need to? The most obvious reason would be that you want to move your installation to a newer and faster SSD
First of all check your actual disk usage and make sure that your installation will fit on your SSD. If you have media such as video#s, torrents etc, these can be removed and stored on external media to be remounted later on. It is important that your core installation is small enough to be moved to the new HDD.
The first thing that you need to do do is download Clonezilla & gparted boot CD’s. Also, have a USB / CD version of your actual Ubuntu / Mint version.
1) Boot off gparted and resize your main / largest partition to make sure that your existing data (All partitions) will fit onto the new drive)
2) Reboot and make sure that everything is still working fine with your system.
3) Boot off Clonezilla CD and make a partition clone of your working hard drive to an external drive or spare hard drive (Not your new ssd!)
4) Remove your working hard drive and install your ssd.
5) Boot off your Ubuntu / Mint installation CD / USB and just proceed with a normal installation on the new ssd drive. (Settings aren’t really important as you will be over writing this partition)
6) Boot off the Clonezilla CD again and restore the partition you created to the SSD, over writing the brand new installation.
7) Reboot into your existing installation on your new SSD!