To connect wit.ai to your facebook page, you just need to create an accound with wit.ai, and then create a new application (or use the default starting one).
Then you can go to the settings of the app, and you will se the Server Access Token code.
You need to paste that server access code in the field "Integrated NLP", that you will find in your Facebook for Developers account, then access the application that you want to use NLP, in the setting for Messenger. For that you must have the messenger app already created and configured with it's webhook wich I guess you have.
Once that's done, the Natural Language Processing (NLP) will be sent to your server automatically as another field in the message. And it's preety simple to understand and train from wit.ai
The messages of the user will be analyzed by wit.ai, and if it finds any entity of the default ones or one defined by you training the bot from wit.ai, will send it to messenger, and this one will insert the NLP in the message.
So you will recive a normal JSON message from messenger, with an extra field called NLP that will contain something like the following example:
"text":"reservar una pista","nlp":{"entities":{"tipo_cita":[{"confidence":0.98398202482107,"value":"pista","_entity":"tipo_cita"}]},"detected_locales":[{"locale":"es_XX","confidence":0.9935}]}}}]
My chatbot is in spanish, but there's an example of how you can see the NLP in the JSON message.
I introduced the text: "reservar una pista"
And it recognized the value: "pista" with a confidence of 0.9839. Wit also detected the language "es_XX" that's spanish with a confidence of 0.9935.