I recently had a trigger spring break on my Ruger revolver. The symptoms were that the trigger would not reset without my manually pushing it forward with my finger, but the revolver otherwise functioned as normal.
I'm not going to go into details on how to disassemble the revolver. You can find a PDF of an older edition of Gun Digest's books on disassembling revolvers here which contains instructions. And here a couple videos covering the disassembly and reassembly:
Note that these instructions are for a complete disassembly--if you are replacing the trigger spring, you don't need to completely tear down the firearm; you only need to remove the trigger assembly. Basically, you just need to remove the stock, pull the trigger, capture the hammer spring by inserting a pin or paperclip through the handy hole on the plunger, and remove it as a unit. Remove the hammer and the pop out the trigger group. Then concentrate on disassembly of the trigger group.
|Staring at the revolver wondering what to do.|
|First step: remove the stocks or grips.|
|Second step: At the bottom of the hammer strut is a small hole. Cock the hammer and put a pin through the hole to capture the spring for removal. I used a straightened out paper clip.|
|Step three: Lower the hammer and then lift out the spring and rod. Pay attention to the orientation of the main spring plate because it will need to be replaced in the same orientation.|
|Step four: Push out the pin holding the hammer and lift out the hammer.|
|This is just another view of the trigger, showing the other side where the pawl connects.|
|Another view of the trigger, showing where the detent and spring for the pawl fits.|
|This is one way of locking the vice grips onto the trigger.|
Disassembly is easy because the trigger is not under tension. To remove the trigger from the trigger guard, push out the trigger pin and lift the trigger out of the guard. The pawl that turns the cylinder and the transfer bar are both attached to the trigger. These just pull off, but be careful removing the pawl because there is a detent and spring behind it. Remove those as well. To remove the old spring, push out the bushing through which the trigger pin goes.
|Trigger Spring (Source)|
Reassembly is more difficult because everything will be under tension. The trigger spring (see photograph) has two tails--the shorter tail fits into a slot to the rear of the trigger and the long tail fits into a slot on the front of the trigger and extending into the trigger guard piece. The trick is pushing the loop down far enough that you can insert the bushing and capture the spring.
Fortunately I had ordered a backup spring because I ended up partially flattening the loop on the first spring just trying a brute force method using a pair of vice grips to try and compress the spring and push it down.
What worked was this: I used a pair of vice grips to hold the trigger. I clamped it with one jaw on the rear of the trigger piece, and the other jaw on the front of the trigger piece. When clamping it on, make sure it doesn't interfere with the long tail of the spring and that you don't mar the trigger. With your other hand, push the spring down into the trigger just enough to slide a punch through the opening to temporarily capture the spring. With that in place, it is much easier to push (actually, pull) the coil downward, using a screw driver to nudge the tails on the spring should they catch on the metal. Once it is pushed down far enough, you can slide in the bushing. With the spring captured, the rest of the reassembly should be straightforward. Just be careful with the detent and spring behind the pawl that turns the cylinder--it can and will shoot across the room if you aren't careful.
One thing that helps with installing the detent and spring is to push the pawl forward enough to allow the detent and spring to be inserted in the detent hole, push the detent in with a small flat head screwdriver, and then swing the pawl into its correct orientation to capture the detent as you remove the screwdriver tip.
When replacing the hammer, pull the trigger fully to the rear. This seems to help getting the hammer correctly oriented. After it is in, slowly drop the hammer. Then you can insert the hammer pin.
Update (1/9/2021): I have included more photographs to show the disassembly process and some additional comments about reassembly.