Online gaming lag

Whenever I play on a gaming server like CS 1.6 or GTA IV, my game lags like my bullets aren't connected with the server. I don't know why it happens and I'm confused if its my computer or internet. I have seen videos on youtube that when a player shoots in cs 1.6 even from a close distance, the opponent still dies from the bullets. How to fix this problem? It happens on all servers

It's hard to say from the limited info above. If it's lag between when you're seeing the action on your screen and when it registers with the server, it sounds like a connection issue (maybe a firewall problem or even just a very, very high ping) but that's just speculation.

A good way to check that is to pack up your computer and go to a friends house (a connection you know is good) or you can have a friend come to you (with a computer you know isn't having performance problems) to see if it runs well on your connection.