From your activity.
If you submit you live in Korea, but your IP address show you're in US, France etc, it will raise a suspicion. If you chat using Spanish language with perfect grammar, it also raise another suspicion.
If you notice a particular user who, each time they login to their account, appears in a new location with a different IP address from their last login, is that not an obvious sign of VPN usage?
This is not entirely correct.
Most people are using dynamic IP address which make your IP address keep changing even you're didn't move to anywhere. Let's say that you're live in Los Angeles, but your IP address could show you're in Washington, Dallas, Boston etc.
The first part is not that simple. Most VPNs allow you to always choose the same region to login from, so you can actually pick a small country, like Luxembourg and constantly connect from there.
How many servers are there going to be in there?
Dynamic IP is also a thing with your everyday ISP. You may have different addresses each time, just that they will always be from the same location.
The most obvious thing is when you lose connection to the server. In such case you will start the VPN, enter the site, but after a while either the program will crash, or the target server you're being routed through goes down and the system will either reveal your real IP, or, more likely reroute through another server, possibly in a different country, so you will log in from country a, but later start connecting from country b.