Go to your Friends list. There's a drop down that shows all channels you are a member of. If you're a chan-op for one of them, that channel will show six buttons, one of which is "Invite". You can use that to invite a player to that channel.
Or use the chan_invite slash command.
/chan_invite channel username
List of all slash commands at Paragon Wiki:
http://paragonwiki.com/wiki/List_of_Slash_Commands
I belong to Freedom TF and Freedom channels, primarily to get teams/leagues, TF's and the like going or for badges. One of these channels apparently has assigned me some sort of status to invite people to the channel since I got two tells yesterday from folks asking me to invite them to the channel. My understanding is that you just plain old "join" a channel, that you don't need some sort of special invitation from a member. But I could be wrong.
So that's my question. Do some channels require that you be invited by a member in some special standing? And if so, how do you make that invitation? I tried all kinds of right-click in various parts of the chat window, tabs, player handle, etc and never saw anything about "invite to channel" or the like.