Here is the official documentation from Unbounce in regards to webhooks. Including an example PHP script.
Overall, it's pretty straight forward and you just need to look at your 3rd party API for authentication, what fields it requires and the field labels.
Couple of tips:
Make sure you don't have any DDoS protection on your server. It might be turned on by default from your hosting provider. I spent hours one time trying to figure out why a webhook was getting passed to the client's server but never actually executed.
The data from Unbounce is URL encoded. If you are using anything other than the sample PHP script you might have to adjust for that.
My company has done dozens of these so if you run into problems, PM directly for a quote.