A pin punch and a large blade screw driver w/a V groove in the blade.

Tighten the trigger plate screws down so there's a little pressure on the lever spindle as already pointed out.
You should be able to feel the safety engaged correctly at this point.

Take a shop rag/cloth w/a small hole in it and place it over the spindle hole to avoid any marring of the frame and trigger plate.

Place a pin punch in (I see allen wrenches seem to be popular now),,lay the screwdriver against the punch and push on the screwdriver handle with your stomach.

That leaves both hands free to push the trigger plate down into position as soon as the spindle lines up.

There's no need to panic doing this, you can push and hold the spindle in position very easily while you use your hands and eyes to line everything up.

Use the thumb of either hand to hold the screwdriver blade down flat against the frame if you like.
Many people that first try this method have a feeling the driver is going to come flying upwards and off the punch. Keep it horizontal, and keep a thumb latched over it and you'll be and feel very secure.

After doing this a few times you'll find it's not necessary to hold it there if you use a pin punch as the punch tapers outwards/gets bigger above the driver and keeps it in position down on the frame.

Keep a finger of one hand below the action on the top surface of the lever. That'll keep from pushing the lever back out position and off of the heavy spring.
The linkage keeps it from coming right out of the frame, but there's enough movement usually to allow it to skip off the spring if pushed far enough.

The trigger plate will snap into place. Remove the punch and cloth.
Place the small spindle screw into place and tighten most of the way to avoid the spindle creeping away and allowing the spindle to snap out of the recess where upon you'll have to do this all over again.

Tighten the trigger plate screws,,relax.

Takes much longer to type out or even to read than to do.
This was the method used at the factory and shown to me while working at Marlin to reassemble LC Smiths.

If there was anything special about the tools used, some 'smiths made up their own special 'slotted screw driver tool'.
They used an old worn flat file for the bit (annealing and shortening/shaping as needed) and used a small bit-brace type handle instead of the normal small diameter screwdriver handle.
Made for a more comfortable time of it!
But it isn't really necessary to do the job.