Find IP Address of Remote Computer

Ok, so I would like to know how to find out IP address of a remote computer over internet. I know about getting the user to my site and logging their IP address, but I am looking forward to more intuitive method of getting the target's IP. Directing the user to my site is not the best way to get the IP for instance the user will get suspicious when asking hit to visit a site for no obvious reason, moreover anyone with even a slight knowledge would figure out the reason. Also it fails if target has dynamic IP. Well you don't expect the user to visit my site every time his IP changes. Is there any method of knowing the target's IP without raising any suspicion like though chatting through facebook or other social media?