When I cleaned my Silvia I simply followed the instruictions on the espresso cleaner packet i.e I dissolved the cleaner into the water tank and ran it through the tank, pump grouphead until all gone and then flushed a tank full of fresh water through. Backflushing with a little cleaner in the blind filter is a good idea. I lock my portafiller in with the blind basket (with cleaner) and run the brew switch for maybe 5 or 6 seconds until I hear the pump change pitch which indicates the system is pretty well pressurised, then switch the brew switch off which releases it all through the 3 way valve. Note however that IIRC backflushing is not recommended by Rancillio for the Silvia. I feel that the occasional backflush is OK and it sure clears out a heap of crap.
You will need to remove the showerscreen too for a clean, best before all the flushing is done. This can be tricky as they are sometimes really tight and its easy to slip with a blade screwdriver and damage the screen. Try using a socket head to unscrew it before a screwdriver. Also, I found that removing the screw when the machine is warmed up is easier - but bloody hot!. The screen is easily cleaned once removed. I think I use warm soapy water.
The rest like getting rid of grinds up in the grouphead seal is straight forward and if you clean after every use like I do you will find there is not much up there.
There should be more info on this site and other about cleaning, have a good read first.