When you approach the hospital from (Hunters Bar roundabout), bottom of Ecclesall Rd, you reach Glossop Rd. Red line on my diagram.
Turn right, then follow the yellow line to the multi storey carpark entrance.
If you have people to drop off first, take the left turn red route and follow blue line to the main entrance, white circle. Then follow purple line to carpark.
The yellow circle is another entrance to the hospital on the same level as the carpark entrance/exit. It's one or two floors lower than the white circle main entrance. The entire place is on multi floors LOL :-)
Pink line is exit from the carpark. Exits the same way as the blue entry way.
Green line is route back to Hunters Bar etc.
White line is from the main ring road that comes up from the end of Bramall Lane area.
Collect a parking ticket on entry and take it with you. When you are ready to leave, the Pay machines are located just inside the carpark entrance. Here's the stupid bit. There's one footpath entrance for floors, A,C.E,G etc, and another for floors B,D,F.H etc. But the pay machines are on entry A, I think. So you might have to walk in one door, pay, walk back out, and then enter the other door. Only in Yorkshire
Hope this helps, even if only a bit