How to increase capacity assigned to Linux Mint

Boot the PC using the PCRepix LiveDVD, then start GParted. Now you can resize and move partitions with it.

It would be advisable to first make backups. For that you can use CloneZilla or Partimage, which are both on that DVD too:

http://pcrepix.sourceforge.net

Is the Mint installation on a physical harddisk or a virtual (VMware or alike)?

It is on physical hard disk, I installed it alongside Windows. I do not run it within windows on a virtual machine

Then you need to repartition, as advised in the first comment above.

if you don't have the pcrepix dvd, any live cd around including mint's should do the trick.

if you need to, you can even use your existing OS : boot in single user mode, mount /usr read-only, run gparted in text mode.

you can also do part of the job from within windows. you won't be able to move the windows partition ( but you'll be able to shrink it ). if you run parted for windows, you can play with the linux partitions as much as you want, if not, you'll need to run growfs on the filesystem after you extended the size of your partition. in that last case, remember that you can only grow the filesystem if the partition was extended towards the end of the disk ( right hand side on any graphic tool )

depending on the situation, you may rather want to create an additional partition, cpio for example your /home onto the new partition, and then mount it on /home

also remember that moving your partitions around can break the boot process. it won't if your ( i assume grub but the same applies to many loaders ) is configured to use partition ids rather than disk offsets. in case of doubt, do not move the partition or add any partition before it, or be ready with a separate cd that you can boot your mint from. 'the super grub2 boot disk' it the kind of stuff you want