How do I create private chatrooms?

All channels are public by default. Anyone can see its users and join the conversation. In a list of channels you can see a public channel's topic.

An Invite-Only channel can only be joined if you are invited by one of its channel operators.
To temporarily make your channel invite-only type: /mode #channel +i
To ensure the channel is always invite-only use: /cs set #channel mlock +i
To invite users to the channel type: /invite user #channel
To invite yourself to the channel use (if you're on the access list) /cs invite #channel

Private channels turn up normally in the channels list. People can see you are on a private channel somewhere, but they can never find out on -which- private channel you are unless they search all (private) channels by brute force.
To temporarily make your channel private type: /mode #channel +p
To ensure the channel is always private use: /cs set #channel mlock +p

Secret channels do not show up in a channels list and you cannot find out its topic unless you join it. If you are on a secret channel, someone who is not on the same channel can't see that you are there.
To temporarily make your channel private type: /mode #channel +s
To ensure the channel is always secret use: /cs set #channel mlock +s

You can combine these modes to make a channel Private and Invite-Only (+pi) OR Secret and Invite-Only (+si) but not both Private and Secret.

Before restricting your channel by using Invite-Only, Private, or Secret please see the FAQ topic, Why are secret channels bad?.