Open a command prompt (start -> run -> CMD)
Navigate to C:\Program Files\Update Services\Tools.
Create a new directory on the root of the new drive -> D:\WSUS\wsuscontent
Then type the following command: wsusutil movecontent D:\WSUS\wsuscontent C:\WSUS\wsusmove.log
If you need to move the database here is a good article on how to do that: Link