There are several ways you might go about this depending on your level of anxiety in doing this. The first question though is; In the Linux filesystem hierarchy, /var and /home are supposed to be apart. Do you have another drive you'd like to install? Would you like to make /var OR /home bigger?
I have not had great sucess with the only partition utility I know of for Linux, 'parted'. The interface is quite hard (for me) to understand, though it is supposed to be quite powerful. If you had access to the Windows tools 'Boot Commander' or 'Partition Magic' they could be helpful. The ext3 file system is ext2 with a journal, and the above utilities understand ext2 filesystems. If you had a CD-burner, you could back up your /home and /var partitions (in case you had databases or a web server running) and repartiton from a boot CD. If you had enough space on another partition (/usr) you could backup the files to a directory structure there, boot from a CD and repartition. In any case I have given you generalities and not knowing what your specific needs are that's about all I can do.
Just remember if you want to keep things, backup before you do ANYTHING!