How my mom started and got to this point as far as casting these (among many others). These are lost wax castings, but the actual start has a bit more to the story.
With the large dogs (she is currently working on an even larger one) clay was used to sculpt the basic dog and fur, but leaving room for modification. From the clay, a silicone mold was made into which wax can be cast. From there, she uses a heated waxer tool (like clay working tools) to finish each with it's own personality. She had even removed heads in order to change the direction the dog is looking. Once the creations are to her liking, the wax forms are sent to one of two casters (the really small ones go to one---jewelry size, while the larger go to a second).
The casters then attach wax sprues and vents and make a tree of the things. Once treed, the assembly is dipped in investment (a heat resistant plaster like stuff) in multiple layers. Once dry, the investment tree mold is placed in a kiln to first melt most of the wax for recovery, then heated to a higher temperature to burn out the remaining residue. This also pre-heats the mold. Bronze is then pored into the main sprue and the workers make sure that all the vents fill as well. This assembly is then left to cool slowly.
Once cool, the investment is broken away, the sprues cut, and the final parts are cleaned, usually finished by bead blasting. Even after cleaning, my mom still has to pick away at bits of remaining investment.
There is a lot of detail work to clean up the imperfections where the investment did not quite fill, or cracked and left flashing. Her Foredom rotary tool now becomes essential and has paid for itself and its replacement flex shafts a few times over. Once the detail work is done, then she lightly "buffs" the pieces with fine maroon ScotchBrite wheels on her old Craftsman benchtop buffer/grinder.
The final patina, to get the dark color of the Irish Water Spaniel coat, she uses liver of sulfur, and again lightly buffs to bring out highlights.
BTW, she will be 90 next summer.