Traps appear as arcane signs or piles of flesh and bones. Not all spots like that will be traps, but many will. Running over them will stop and lock your current warrior into that spot. Most traps impose a minor penalty, but some give a minor buff.
You can spend a movement point to do a perception check and maybe spot traps, but it's not usually worth the movement point.
Note that credit towards this achievement is made if your character resists the trap. Most warriors have 0% trap resistance, but can gain some through skills. The DLC Master Smuggler has 100% trap resistance and a lot of movement speed, so she can be a huge help for this achievement.