In order to begin working on the Remove Trap skill, your character must have at least 50 skill each in Lockpicking and Detect Hidden.
I believe you start passively detecting faction traps with 80 Detect Hidden skill (assuming your character is in factions). (Passive detection means you see a message that there are traps in the area; the color of the message denotes the type of trap.)
I believe the passive detection works over longer distances the higher your DH skill is; however, it's been a long time since I've had a character in factions with DH skill at anything lower than GM. For that reason, I also can't tell you with certainty if 80 is also the minimum for actively detecting faction traps (i.e., using the skill on a targetted area). I believe it is, but I'm just not sure.