First, you must have a private park location. You can create it using API or using the service web portal. Then you can park a call to a private park location using the call transfer API with the park orbit id (created above). After transfer a call to a private park location, you will need to save the telephony session id and the new party id (returned by the call transfer API).
Then to pick up that parked call, you need to know the device id (make sure that the device is online) of a user who wants to pickup that call and use the /pickup API to pick it up.