Howdy
If you simply want to pull the cylinder out, for cleaning, without taking the entire gun apart. This is all you have to do.
First, pull the hammer back slightly to the half cock position. This draws the bolt down into the frame, freeing the cylinder to rotate. With the hammer at the half cock position you can pull the latch back to rotate the barrel down. You cannot rotate the barrel down with the hammer all the way down, at least not with the originals.
There are two screws holding the barrel block in place. The barrel block has two tabs on the bottom that prevent the cylinder from sliding backwards. Leave the forward screw in place, do not remove it. You may need to loosen it a tad, but just leave it in place. On the this original, the rear screw had a flat ground onto the shank. Turning the screw one half turn freed the barrel block to pivot up. Notice there is a witness mark next to the screw indicating the correct position of the screw to latch the barrel block down.
I don't know if the modern replicas have a flat on the screw or not. In any case, if turning the rear screw one half turn does not free the barrel block to pivot up, then remove the rear screw only. Leave the front screw in place, maybe loosen it a tad. That is how they were designed. That will allow the barrel block to pivot up as in this photo. Notice the barrel block has rotated up to a stop formed by the semicircular cut for it in the top strap. With the barrel block pivoted up the cylinder can be pulled straight back off the cylinder arbor for routine cleaning. That's all there is to it. As I said, you may need to loosen the front screw a tad to allow the barrel block to pivot up. To put it back together again after cleaning, with the hammer still at half cock so the bolt is withdrawn into the frame, put the cylinder back in place, lower the barrel block, screw in the rear screw to secure it and snug up both screws. I do recommend hollow ground screwdrivers that fit the slots well, so you don't bugger up the screws.
After production of the Schofields ceased in 1877 if memory serves, S&W simplified removing the cylinder. The Schofield style latch was done away with. This New Model Number Three shows the newer latch. There was a single tab on the bottom of the latch that retained the cylinder. The latch was spring loaded. Lifting it up allowed the cylinder to be removed. There was an interrupted thread on the rear of the cylinder arbor. Holding the latch up with the thumb, the shooter rotated the cylinder counterclockwise as seen from the rear, while exerting slight backward pressure on the cylinder.
This allowed a matching thread in the cylinder to engage the interrupted thread and the cylinder could then be pulled free. Much simpler than the Schofield system, no tools needed, the cylinder could be quickly removed in the field if necessary without any tools.
The rear sight of these revolvers was two nubs protruding up from the 'tang' of the latch.