Firstly, the players need to define why and where they are wanted. It may just be outstanding fines in one city, in which case he needs to keep his head down when the local authorities are in sight. He may have murdered a noble and a bounty has placed on his capture. This requires staying low pretty much everywhere he goes.
Whatever the player decides, it has to be okayed with the Marshal/Game Master. If it's so insignificant that it would never come up during the game, then it's not a hindrance. The GM can also decide whether their description warrants a minor or major hindrance. A Wanted (Minor) character would be harassed in many places, or actively hunted in one region. A Wanted (Major) character would be hunted wherever he goes.
So going off of the Wanted description the GM and player agree on, it should be clear in what regions the hindrance comes into effect. A confrontation could occur any time the party gets the attention of those seeking him, or maybe just by failing a random roll (eg. a Stealth test daily to avoid casual detection.) By timing the encounter, you can make things very interesting. (eg. Police enter the bar you're in while you're in an important discussion with an important NPC.) If they're wanted by the organisation they're actively trying to disrupt, then the organisation is applying special attention to capturing them, perhaps even outsourcing.
Someone who takes the Wanted hindrance is asking (whether knowingly or not) for more problems.