Apply for a vacancy I suppose, but you'd need to have a fair bit of experience for one with a major firm. Never really thought about it but I'd guess most odds-setters and traders start out as trainees, & you'd probably need an A/A* in A-level maths at the very least to get a foot in the door.
Spot on - some firms don't even have a specialist odds-setter for politics, they just draft someone in from elsewhere when necessary. Ladbrokes were actually advertising for a new politics odds-setter on Twitter the other day, must have been caught out by the snap election. All they can do is...