The traps will have a subtle visual change in appearance. Some more obvious than others.
Lightning Rods should be the easiest to spot. When inactive, the rod itself will be on its side. When set, the rod is pointing up into the air with sparks and will have a slightly audible electrical hum. It will only affect enemies if they step close enough. It will trigger after a short delay. It can be disarmed by shooting at it.
Spike traps can be just as noticeable if you are observant. When set, a tripwire will be strewn across the pathway and the handle will be down. If walked across, the player will be crushed by the spikes instantly. This affects all players, even yourself! It can be disarmed by shooting at the rope or using the handle again.
Snares are much more difficult to spot. When inactive, you will clearly see the rope on the ground and you will see many loops. When set, it will be slightly transparent, have less loops and the noose is connected to the piece of rope going away from the coil. If walked across, it will ensnare the player raising them up in the air hanging. When ensnared, they can escape if the rope is shot. I don't think they can be disarmed however.
(the rope is outlined here just for visibility, it will not be as visible in the game)
Player laid traps (Land Mines or Fake Ammo Boxes) won't be as easily noticeable. They will trigger after a short delay before detonating. You'll just have to pay attention to the ground and remember where pickups are in the map. It can only be triggered by enemies. Out of place ammo boxes should be obvious. Just don't move too slowly or you'll get caught by the blast.
In general, it helps to know where all the traps are in the map so you don't accidentally walk into one that's set. At least you'll be prepared to ignore it or be cautious.