The most common way is to actually affect the player when the simulated attack happens on the player's machine.
This means that the player may "snap back" in high-action sequences. For example, player tries to dive behind a corner, other player shoots, player sees on the screen diving into cover, but is then snapped back and lies dead on the floor right before the corner.
This is an inevitability of the transmission time of packets (speed of light.) The trick is to choose combinations of game networking strategy and game design themes to make the trade-off as acceptable as possible to players.
The latency can move around in the system. For example, you could refuse to move the player until the command comes back from the server. This means that the player will never see anything "wrong," but control latency will be higher. This mechanism is often used in RTS games, as well as games with slower command rates like click-to-move RPGs and navigating large heavy spacechips.