Colt, AMT, Randall, Coonan, Star
I don't have an STI, but I have a couple of different makers' 1911s and here's how I do it:
I insert the slide stop SHAFT into the frame and barrel link with the rest of the slide stop hanging down in the trigger guard area. Then, with the slide stop pulled out 1/16" or so, rotate the end of the slide stop up to where it meets the spring plunger and start the engagement process.
The slide stop is just outboard of and below the spring plunger.
Usually, just pressing with my thumbs upward and inward it pops into place.
I have occasionally had to use the point of a small lever to ease the spring plunger in just a bit. Right hand with the lever, and left thumb continuing to push the slide stop.
I hope that helps.