While in the conversation dashboard, there are a number of keyboard shortcuts available to help you navigate around the window without need for a mouse. Below is the full list of available commands.
n - Press n to enter the new message control. Once you've typed a number or name, you can use the arrow keys and enter to traverse and select the contact you want to send a message to.
c - Press c to focus on the text input box in the conversation history and compose your message.
d - Press d to toggle the details sidebar open or closed.
esc - When in the compose message box, hit esc to lose focus on that box.
up / down / j / k - When you're no longer focused on the compose message box, you can hit the up and down arrows or j and k to move up and down the different conversations in the conversation list.
s - Press s to bring up the conversations search functionality.
If you're lost, here's a few gifs to help showcase how a few of the above work:
N for new message
C to compose