A little background - this one is intended for people with no background in working on bikes. If you've worked on bikes you probably don't need to read this. If you haven't this should be clear enough for you to be able to get it.
Balance bikes are the trend in teaching a kid to ride a 2 wheeler. The idea is to allow them to learn balance before they have to coordinate pedaling. There are very nice custom bikes built specifically with this in mind. However, they tend to be a little spendy and when your kid is ready for pedals you've got no choice but to buy an entirely new bike.
There's a pretty good background of what I'm talking about here:
Step 1: Tools and Getting Started
I was unable to find any 12" bikes that didn't need a lot of help locally, but get one used if you can. Kids usually outgrow this size bike rather than wear it out.
To do this you're going to need a 12" adjustable wrench, a chainbreaker, and a screwdriver. If you have a used bike you're going to want a pedal wrench.
Our objective is to remove the chain and cranks. If you're starting with an assembled bike, remove the training wheels and the pedals - note that the left pedal is reverse thread. You should probably use some penetrating oil before trying to remove them.
Step 2: Remove the Chain Guard and Chain
On this bike I needed to remove the chain guard to get to the chain.
Once you have access, use the chainbreaker to remove the drive chain.
Step 3: Remove the Crank
Next turn the bike around and take a look at the way the cranks are held in - on this bike it is a one piece crank held in with a single nut that was reverse threaded. Remove the nut, washer, and the bearing cup. Remove the bearing (this one is caged, thankfully) then remove the crank.
Step 4: Clean Up the Bottom Bracket
Clean all the grease off of everything and put the bearings, cups, washer and locknut somewhere for safekeeping - you'll need them to put the cranks back on. On this bike the edge of the bottom bracket was nice and smooth so I just left it as it was, but if the edge of your bottom bracket is rough you'll want to put some tape or a hunk of innertube on there to keep it safe.
Step 5: Finish the Build
With the drivetrain off I still had the nasty chainguard stays sticking out of the bottom bracket so I put the chainguard back on.
From here if you have a bike that was already built you're done. If there are any brakes you might want to remove them but it's not important. If you have a new bike, finish building it according to the directions you have.
Keep in mind that this size bike is not intended for riding on roads and that with the drivetrain off it has no brakes! Always have your kid wear a helmet.
Once your kid is comfortable riding, stopping, balancing, and turning you can put the pedals and crank back in.