Create a folder called "recaptcha" in your my-plugins directory. Unzip all files into that directory.
You will need to sign up for a Recaptcha Account. You can do that at https://admin.recaptcha.net/recaptcha/createsite/
On signing up, you will receive two keys, a public key and a private key. In the bbpress admin, browse to Plugins > reCaptcha bbPress, and put in the public/private keys in there.