Gunhacker's picture shows the position to allow the slide stop assembly to be removed from the gun during field-stripping.
Having watched innumerable folks having trouble trying to field-strip their 3rd gen guns at a cleaning station, the single most common "problem" I typically see is that they initially align the slide & frame properly ... but then when they shift their attention over to the end of the slide stop pin (on the right side of the frame), they unintentionally allow the slide to shift out of position to allow the slide stop to be pulled free. This results in trying to push steel through steel, and you're going to tire out before the steel ever yields.
Being right-handed, I usually grasp the gun in my right hand (left side facing me), with my right thumb under the frame tang and my fingers wrapped up around the slide, in front (and against) the rear sight base. That allows me to easily "squeeze" & pull the slide rearward, and then hold it still while reaching around and pushing the slide stop's pin from the right side.
Yes, sometimes a slide stop might have a bit of roughness that makes it stiff to start moving past the guide rod's plunger, and the end of a plastic pen or plastic (or wood) handled brush may allow a bit more pressure to be exerted against the tip of the slide stop's pin. No need to start using steel tools and hammers, though.
Getting the slide stop back in the frame also seems to give some folks no little bit of frustration at the cleaning stations, too.
Holding the frame and slide aligned in the same manner as when being disassembled, you need to make sure the barrel lug isn't getting in the way of the slide stop pin as it's being pushed in the frame. (Look through the frame hole and see if you can see the edge of the barrel lug partially visible through the hole. If you can, it's going to be in the way of the pin as you try to push it through the frame.)
This is most easily done by either tilting the muzzle upward (so gravity shifts the barrel rearward just enough to clear the hole in the frame), or, holding the pistol level (horizontal, with the left side of the frame facing "up"), gently push the muzzle end of the barrel rearward, which will also move the barrel lug clear of the hole in the frame.
Otherwise, a bit of the barrel lug can block the frame hole for the slide stop pin ... and you're going to be pushing steel against steel again, and the gun won't tire. I've seen some folks using a scary amount of effort trying push their slide stop pins into that bit of barrel lug blocking the frame hole.
Naturally, aligning the slide stop's rear tab is also necessary in order to push the slide stop fully into position. In an occasional gun it might be helpful to reach up and gently push in the slide stop's plunger, so it slides over the side plate (I've mostly noticed this to help in the .45's).
While it doesn't seem to happen very often, I've found a few guide rods that had developed a burred (rolled) edge on the plunger which made it harder to push/pull the slide stop pin past them for disassembly/reassembly. I don't know if that was from some user/owner banging away while trying to "hammer" their slide stops out or back in, or just one of those "wear" issues that sometimes seems to eventually develop.
