This demo page is a full working reCAPTCHA example for how you can use reCAPTCHA API in your own web application. The code is very similar to the code I have used in my WordPress comment form tutorial. The example works simple: 1) Click the reCAPTCHA checkbox, 2) enter some text (not HTML into the textarea and 3) submit the form by clicking the "Submit" button.
The PHP code for this reCAPTCHA example is a bit different from the code I've used for my WordPress tutorial. Click here for the example code.