Once you have customised the clan chat list you should now begin to see the clan chat on your screen. The clan chat is usually a different colour to your regular chat and can come either in the "all chat/global chat" or you can drag the clan chat box out to make the clan chat be displayed in its own box.
However, if you make it display in its own box, you will need to turn off the filter on the "all chat/global chat" interface or you will see the clan chat twice.
If you can't see the clan chat in your "all chat/global chat" this also means that you may have the clan chat filtered from your chat box. The filters of the clan chat can be found in your ribbon bar above your chat screens, the icon for the filter looks like a 3 little men icon. If it's golden then the chat is on, if it's grey then the chat is off.
Please also keep in mind you may not see the ribbon filter buttons if your chat screen is too small, they would then get hidden behind the (-) icon and you will have to stretch your chat box to be able to see the filter buttons again.
You can talk to the clan chat using the // shortcut before any message in the "global chat/all chat" or if you have the clan chatbox separated you can just directly talk by clicking on the clan chat box.