Okay, so I want to re-install Ubuntu, but in order to do so I'm being told to delete my previous Linux partitions. However, I can't tell which one's to delete. The only one I know for sure is the Linux swap, because it has Linux in its name. How do I know which other partitions I can delete, without screwing up Windows 7?
You can identify Windows 7 partitions by those that are called "ID/Type 07: HPFS/NTFS". Rarely, Windows 7 systems may also have partitions with type "vfat". Leave those alone.
Linux partitions will have ID 83 (types can be ext2, ext3, ext4, etc.), and ID 82 (Linux swap, as you noted).