When the private show feature is available, the blue Start Your Show Banner will appear next to the tipping tool beneath your model's video feed. Click on it, and a pop-up will appear summarizing the models per-minute credit rate for a private or multi-user session. Click Start Your Show within this pop-up to begin your show.
Once in your show, you can chat as normal, though no other users will see the video feed or the chat exchange. Above the chat interface, a countdown timer will appear to let you know how much private time you can enjoy based on your current credit balance.