Sometimes the thumbpress on this older model of Schlage handleset gets all lopsided and then the latch won’t retract far enough to open the door. The repair is not that difficult and requires no parts. This isn’t a thorough step-by-step but with the photos, a few tools, and the right amount of confidence, I think you can sort this out.
The issue is that a roll pin comes loose from one of its two anchor points. To get to it you must first take the handleset off the door. If your handleset has a nickel-sized through-bolt cap below the knob on the interior side, somewhere along the edge there’s a break where you can use a small screwdriver to pry it off; there’s no reason to scratch the paint in doing this. Once the handleset is off the door, remove all four screws that you see. Pay attention to how everything is assembled as you go, since you’ll have to reassemble it when you’re done. Once you get to the roll pin, push it back through the hole it slipped out of. You could use some tongue-and-groove pliers for this. Then—and this is important!—use your pliers to crimp both ends of the roll pin so that it can’t come loose again.
Now put it all back together. As soon as you have the thumbpress reaffixed and one or two of the other screws back in, test the thumbpress for springiness. If it’s not doing what it’s supposed to, back up and try again. The part that’s potentially confusing during reassembly is the position of the spring. The free straight end should be pointing toward the top of the handleset. When it comes time to mount it back on the door, make sure to rotate the spindle so that the bulbous side is closer to the edge of the door. Otherwise you’ll find that the thumbpress is hard to depress, and then people in your house with less grip strength will complain.
That’s it. You can do this. Godspeed.