Here's a break down for the 610,612,620,712,712,912. They are pretty easy models to tear down and clean. It also applies pretty good to the Beretta Xtrema line and the Weatherby SAS (Valtro).
Pull the bolt back so it locks in the back position. Remove the magazine cap, forearm, barrel, and the piston. Let the bolt go forward slowly and when almost all the way forward and remove the bolt handle by pulling it straight out of the bolt body. Now the bolt/action arms/gas sleeve assembly will slide out of the front of the receiver. Turn the bolt body assembly to the side and press the firing pin in slightly. The cross pin in the back of the bolt should fall out and you can now slowly let the firing pin and spring out of the back of the bolt body. Turn the bolt upside down and push slightly on the bolt face to release the pin that bolt face rotates on. Now the bolt face can be removed from the bolt body. Knock out the two pins for the trigger group and pull it out of the receiver. Remove the magazine spring retainer from the end of the magazine tube. I like to use a pair of snap ring pliers. Caution: The retainer will be under spring tension, so be careful when removing it.
Spray/flush the receiver and trigger group with a gun scrubber and let it soak for a little while. Clean the piston with a solvent like Hoppes or Slip 2000. Clean the rest of all the parts with a solvent and make sure the inside of the bolt body and face are cleaned. Clean the inside of the magazine tube by pushing some patches or paper towel with a little solvent through it, followed by a dry and clean one. I do this at least once a year or if the gun gets really wet. Clean the ports (once a year) with a #.120 drill bit (612/712 models, not sure on the others) by sliding it in and out by hand. Be gentle as not to remove any metal. With a solvent clean the inside of the barrel band/gas chamber and then the barrel. Make sure the barrel extension is clean especially the cut outs where the bolt face locks into. Spray the inside of the receiver down with a gun scrubber or some other solvent. If needed, use a brush or Q-Tips to clean the rails (grooves) in the receiver and around the bolt latch and cartridge stop areas. Spray the inside of the receiver and trigger group off with some compressed air.
Use good oil like CLP, FP-10, or Militec to lightly re-lube the gun. Put a drop between your fingers and lightly coat the shaft of the rotary bolt face and the pin it rotates on as well as the firing pin and spring. Now you can re-assemble the bolt with the firing pin. Lightly lube the magazine spring and re-assemble. Put a drop or two in each rail in the receiver and let it run towards the back of the gun. Put a few drops in the trigger group and blow off the excess with an air hose. Make sure there is a little on the face of the hammer and the carrier dog. Put the trigger group back into the receiver followed by its two pins. Lightly lube the recoil spring and the lower half of the outside of the magazine tube (where the spring rides on). Slip the spring over the magazine tube and then install the bolt body/action arms/gas sleeve. Slip the piston on followed by the barrel and then the forearm. Tighten down the magazine cap and push the bolt handle back into the bolt body. Work the bolt back and forth a dozen times and you should be good to go.