The fastest way to do it is to right click the top border of the chat window. Or hit escape till you bring up the in-game menu, and click chat configuration.
Now, go to the Channels tab in that config window and type in the channel you wish to join.
Let's say the channel is ABC
Type ABC in the box provided and the Join button will appear.
If it still remains grayed out, you need an invitation from the channel admin because it's a priviate channel. Make sure the admin communicates with you on this invitation as the notification is bugged. Once he/she gives clearance, enter channel name again and join normally.
You are recommended to make a different chat tab for each channel to avoid chat flood or missing out on previously posted messages - do this using the relevant tab of chat config.
On to your other queries.
Channels are text only.
Do not bother with the in-game voice chat, use Skype, TS or whatever, they're much better.