You need to copy your new IP address from this page.
Now we're gonna use PuTTY...
enter root@your_ip_address into the "Host Name (or IP address)" text field.
optionally you can enter a name to easily re-load this session later. Enter the name in the text box under "Load, save or delete a stored session" ... I opted to use the name of my droplet (zombizu) in this case. I modified this image a bit to protect the names of other (private) sessions I have saved.
If you opted not to use an SSH key... Just click "Save" on the right and then "Open" at the bottom. You may get a prompt asking you to confirm the connection here... Once you click "Yes" you will be prompted for your password. This would have been emailed to you by DigitalOcean when your droplet was created.
If you did follow all the instructions for the SSH key setup, click the + sign by SSH and click "Auth"
Click "Browse" below "Private key file for authentication" and select the .ppk file you saved earlier. Now, before you clock on open, scroll to the top in the left panel and click on the top option "Session" so you can save.
Click "Save" and then "Open" to connect to your server.
As mentioned above you may get prompted to confirm the connection. Once you click "Yes" you should be logged in. If you opted to use a passphrase on your private key you should enter it when prompted. As I said before, in this example I opted out of the passphrase:
I slightly edited the image but you should see something quite similar.
If everything went well, you are now logged into your droplet and we can really get started.