WD40, Kroil, Citrasolve, Lacquer thinner, solvent, combined with 0000 steel wool in your hands for carbon on the bolt.
BCG, barrel extension/lugs, bore: give them a bath by dunking in either of those above, or spray wash with aerosol WD40 or Kroil.
Wear dishwashing or medical gloves. Wash and blow with compressed air. Snake the bore one pull. Lay the rifle horizontally, or muzzle down.
Do it everytime you shoot it. Except for the right ones, neither special nor expensive tools need be used to clean a firearm that is properly maintained.
You didn't ask about lubricant. Grease. Oil where grease can't go. Shoot and be happy.
Spray. Blow. Lubricate. Fire.