If you want to skip all the fun things you can try, this would be a suggestion;
Boot from a stick.
Find, or create, a new partition on either an external or internal device that is large enough for all the data in your current /home directory. Having enough space on an external device makes the process simplier. If you have data (charts, mp3, videos) backed up elsewhere, obviously it can be smaller as this is a rescue.
For example, a 40GB harddrive all in one partition (two with a swap partition) 25GBs are used.
Repartition 26GBs to one partition, and the remainder to *new* partition, if you have a large swap you can sacrifice it.
When you have a *new* partition, assure it's mounted.
Code:
sudo mkdir /media/snafu
then,
sudo mount /dev/sda3-4-7"WHATEVER" /media/snafu to mount it to the directory you've just created.
Using the filemanager or the commandline move the data from your /home (actually /media/"whatever_the_long_UUID_number_is"/home/) to the new partition/other device (/media/snafu, or name/location of external device.
The point is to have, or create, a space that will accommodate the amount of data you have in your /home directory. It doesn't matter how, or where. It just needs to be done.
Using the example, allocate 10GB to /root and 16GB to /home, re-install the system, adding your newly created partition mounted and named (/snafu, e.g.) so when you boot the fresh installation the partition/file structure is automagially recognised.
Move as much data 'back' to the newly created /home partition. Resize the partitions as required.
When all the data is 'returned' to /home, reduce the lifeboat partition to a swap size and format and sail on.