Basic disassembly same as an 870, 1100 or 11-87.
Put the safety on. Drift out the two pins in the receiver & remove the trigger assembly.
Don't tear it down ... usually no problem there. Soak in varsol or tolulene and blow dry with compressed air. Don't pull the trigger while the assembly is out.
The 58 has an internal piston. As I recall, it comes apart by depressing and lifting the actuating arm oout of the slot by aligning the pin with the hole. The action return spring
is under a lot pf pressure, so control it. 9 times out of 10, yes, it is this spring which has become weak over time and needs replacing, as will the bolt buffer in the rear of the receiver. clean the inside/outside of the piston/mag tube with 0000 steel wool and Hoppe's.
Many 58's were prone to crack the receivers with a lot of use. If yours isn't cracked, consider having a smith mll a relief slot in the back of the cocing handle slot. To see how wide & how long, just compare the slots in an 1100 to your 58.
The 58 has two little holes angling up into the barrel from inside the magazine tube ring. Make sure these aren't blocked with carbon. Same for holes in the end of the magazine tube cap. "H" for high brass/heavy loads, "L" for low brass light loads.
When properly maintained, the 58 is a great gun, and was the favourite of Canadian Skeet Hall of Famer, Barney Hartman. I prefer them to either the 100 or 11-87. They seem to both point and balance much better.
You may be able to obtain some parts directly from Remington in Ilion ... Western Gun Parts shows no listings for the 58. Other than that ???