For newborn pinks I just freeze them.
For anything with fur I either whack, dislocate, or gas them.
Whacking is easy for one or two... grab by the tail and slam down on a table or a wall, hitting the back of the skull... usually this breaks their little necks. Takes practice to get it right. Don't do this with juvie rats.... I did it once and the rat flew across the building and I was left holding just the tail sheath. I felt awful! (and my outdoor cats had nabbed the rat before it could get its bearings)
Dislocating I usually use a flat piece of metal (my mouse-house knife doubles for this task)... Usually the mouse or rat is sitting on the surface of the table, me holding their tail. I often have some treats on the table to try to distract the animal from the eventual doom. While they're munching, and I'm holding their tail, I try to quickly place the knife (blade not in contact with the animal) and jerk up and back... usually I hear and feel the CRUNCH of the successful procedure. Sometimes I don't. (I HATE that). I use this method when I can't get dry ice and have a lot of animals to "off".
Gassing. I find that Dry Ice is the best method for a mass execution. I buy between 1 and 4 pounds of dry ice. (1 pound is fine if I know what animals are being killed and have them ready).... I have a huge 40 gallon rubbermaid. I put some bricks in the bottom, and pour water in up to just below the level of the bricks. Toss in the dry ice so it's in the water, then after three or four minutes I place a critter keeper full of the doomed animals onto the bricks. Usually on it's side so that the gas will come in through the lid easily..... Within 10 or 30 seconds there is no movement inside the cage. I usually am setting up the next batch to go in and prepping my "freezing" materials so that I can process the ones in the "gas chamber". Note: I don't have a lid on my gas chamber, the CO2 is lighter than the surrounding air so does not escape the container. Once five minutes has gone by I pull out the one container and put in a fresh one full of live animals. By the time I have pulled out each animal, shaken off any substrate or animal waste, wrapped them in cellophane and thrown them into a larger ziploc baggie, the next batch is ready to go.