From windows delete the empty partition (unallocated is probably the word they'd use for that so you are good to go).
Start the Ubuntu installation and when you get to the partitioner choose 'install on empty space' or use the manual partitioner to manually choose it (that way you can also set sizes for /, swap and, if need be, /home)
It will look like this:
Regarding the edit:
You MUST create a mountpoint for at least root.
See the / in this image:
From your situation: hit the line that says 'free space'. Create the partitions you need (root /, swap, home, data partition(s) etc) and then hit forward.