Slaughter
You'd think it'd be the easiest thing in the world, wouldn't you? Where's the problem?
I hear you ask, Just give him the chop as soon as you see him!
Wrong, wrong, wrong, wrong, wrong. Like I said before, adrenaline spoils the flavour. You don't want your hobbit to be panicked or scared when you slaughter him. If you rendered your hobbit unconscious when you bagged him, let him sleep it off for a couple of hours. Then, when he's calmed down, stick him as efficiently as possible. This is a fine art in itself: ensure the halfling is rendered insensible, shackle its ankles, and stab up through the hollow of the throat into the heart. Make sure you're wearing an apron as bleeding him out can be somewhat messy. The hobbit should die within thirty seconds. Then, scald the carcass to kill off any bacteria that might reside within, and give it a shave. Luckily hobbits don't have much in the way of awkward hair: just the curly hair on their heads and feet, really, and those aren't particularly nice cuts anyway. Shave them or lop them off. Remove the hands.
Evisceration
Next thing to do is to get rid of the innards. Some of them can be used later -- kidneys, liver -- while other stuff is going to be pretty useless.
First of all, if you intend to joint your hobbit carcass for freezing and serving up in small amounts you will want to split the breast-bone. Use a buzz-saw for this task, or, if you have the skill, a big knife. If you intend to spit-roast the hobbit, you can skip this step. Hobbits tend to be small: three feet tall, and scarcely more than seven stones in weight, so you can leave the brisket intact.
Now it gets messy. First of all, cut around the anus, and lift out the genital cluster and rectum. The bung cut must be performed with precision lest the contents of the bowels contaminate the carcass. The testicles can be saved: as foul as it may seem to our Western sensibilities, they are in fact perfectly edible. Then, cut out and remove the intestines and stomach. You may wish to save these for use in sausages, but personally I advise against it. Being a greedy species, the hobbit is likely to have eaten recently, and cleaning out the intestinal tract is frankly more trouble than it's worth. Then remove the plucks -- the heart, lungs and liver. Hobbits are fond of their pipe-weed, so that pretty much means the lungs are inedible. The heart can be pretty tough, so I wouldn't advise eating that either, although it is edible. Hobbit liver on the other hand is quite the delicacy, as they eat heavily and often. Grill it up as part of a hearty breakfast or make it into a paté. Delicious!
Almost ready for butchery now! If you intend to joint the carcass, chainsaw the hobbit in half. Make sure you get a good, clean cut -- start at the base of the spine, then cut down to the neck, bisecting the spinal column. This is important. The cleaner the cut, the easier it is to remove the spinal cord. The last thing you want is to discover that there's a human-transmittable form of mad hobbit disease. Using a high-pressure hose, or failing that a strong friend to work the water-pump while you aim the hosepipe, wash the carcass out thoroughly. Store in the fridge or ice-house overnight. Your hobbit will then be ready for butchery.