When you download and install the client on to your computer, you are asked to create an account. There's a free account, which gives you 2GB of storage, and paid accounts which offer more storage. The dropbox on Windows gets installed in to your "Documents" folder in your user file.
Install the app on your phone and login to your account where you can view your dropbox. Dropping files in to either the dropbox on your phone or computer will upload them, and can then be seen on either.
It's a great app for sharing files between your phone and computer. The app for Android can be found in the Market by searching for Dropbox and the website for the client is here.