Hey there, :)

click on the coordinats / on the town of that somebody and then select "send message". 

On mobile you can also click someones Name in chat to bring up their statistics panel to then go to the message tab. This option is not there on PC, for some reason, so you need some way of either getting to the town of that somebody (coords) or knowing which clan he/she is in, so that you can go that route.

Clan invites can only be send by Elders & Chiefs of a clan. Its mostly the same procedure as above just with klicking "send clan invitation". :D