I found many of the methods detailed on the net outdated and far more complicated than necessary.
My upgrade was from Mint 14 64 bit to Mint 16 64 bit but I am sure it can be applied to other upgrades.
First back up your data. I am describing a clean install. I find that best as it gives your machine a good spring clean.
I use Luckybackup as the included one does not work for me (stalls on a 'pipe'), a fault documented several years ago and LB is quite fast too. Move data you do not use on a separate drive and delete original off your home folder. This will speed things up.
Backup your home directory with Luckybackup
Add a Task.
Your source directory is /home/(your user name)
I use external USB harddrive so destination is /media/(username)/(drive name)
You can do a dry run to check for errors and if OK do backup.
The drive I had did not like large files as was supplied FAT32. So I reformatted in NTFS
The files can be viewed independently on the external drive. Use CTRL-H to see hidden folders.
See below for Restore process.
Download the ISO of the Distro you want. (in my case Mint 64 bit Cinnamon)
Create a bootable USB stick using the USB image writer tool in the menu.
Boot off the USB stick to the new distro and see if it is what you want.
If all OK click on Install Linux Mint.
Choose 'Something else' option in the menu.
Now you are faced with this menu.
Select the EXT4 partition with your existing distro on it (in this case Mint14) and edit it to bring up the box to the right.
Select Use as EXT4, Format tick box and '/' in the mount point.
Ok and it's clear. (you did back up your data?)
Device for boot loader installation should default to that shown. Leave it like that.
You can now 'install now' to that partition.
Where are you, Keyboard layout and user details entered and you will be there.
Restore your data and you are back in business. I manually re-enter the software which brings it up to date and printers.
Source directory this time is /media/(username)/(drive name)/(username)
Do an update which will be substantial.