Partitioning your disk into 2, C: and D: is effectively the same as having 2 separate disks; there is no mechanism for data to overflow from one to another.
Many people partition their disks to have, say, the operating system and programs on one and their data on the other - it makes it easier to separate and back up the data.
You can manually move data from one partition to the other, particularly if it is free-standing - downloaded music, movies or whatever.
Data related to programs, e.g. wordprocessor documents, can also be moved as the program's options can be changed to point at the new data location.
One thing you might like to do is to see what is using up all the space; often it is the Temp file, which can be emptied easily. There are a number of programs that show you disk usage; one I like is click here
If you install this, you can right-click on any drive or folder and it will show you the size of every folder and sub-folder.
The other big space user is the Recycle Bin; files in this take up their original disk space - they are not removed from the disk until the Bin is emptied.