The trigger is in direct contact with the hammer in a 37. No separate sear for disconnect. The slide takes care of that as it operates back and forth.
To get at the trigger itself, you have to take the stock off by removing the through-bolt in the rear of the stock.
Once the wood is off, take the trigger group screw (smaller daimeter, lower screw on the left side of the receiver/rear).
Pull the entire trigger group out of the receiver from the back.
Now you have to disassemble the trigger group to get at the trigger itself which will be about the last part to come out.
Plenty of springs to deal with but none that can't be handled with just your hands. All coil except the slide stop release spring which is a bent wire thing. Simple pins holding things together.
The mainspring itself is the hardest to handle. It extends down into the rear extention that the stock bolt screws in to.
There's a follower (I think Ithaca calls it the mainspring cup), then the spring, then a small 'cap' behind that that the spring rests against when assembled.
Sometimes that 'cap' sticks in the bottom of the hole. Not a problem as long as you realize it's there and doesn't fall loose and get lost while you're dealing with the repair.
FWIW,,The machined channel in the trigger group that the trigger is given clearance to move downward when pulled sometimes gives problems.
It's a perfect catch place for an errant BB from a poor reload that might spill some shot while being worked through the action.
A single small pellet, even a #9 can roll down that 'ramp' and the gun is out of action. Pulling the trigger feels like the safety is stuck in the ON position.
I've put several back in action from the problem at a local skeet range,,one of mine included!