Well - if you are speaking about the HubSpot app all responses will be show in the conversations inbox view if someone starts a chat.
But in general this is how it works:
1. In your HubSpot portal you set up a chat (it will be branded with HubSpot if you are a free account and non-branded if you have Marketing Starter of higher).
2. Once this is set up - its very easy to put in a one line javascript code on your site - and this will make the process of get the chat "in place" extremely smooth.
That javascript code will be shown in the portal once you have created the chat.
3. Usually the chat will be opened in a browser and it does not matter if its on a phone, tablet or a webpage to do so.
4. In your portal you can create bot flows and collect data using bots.
From an API perspective
More info on what you can do using the API to connect to the HubSpot chat or the HubSpot convesation can be found here:
(NOTE: You might need a sales professional access in order to use some of these workflows - im not really sure exactly on what pack you need it but Workflows is in either marketing pro or sales pro an above)