Assembly
Be sure that all surfaces to be attached are clear of irregularities, the surfaces to be glued must meet together easily. Sometimes the improper drying and warping of wood can make a surface a bit cupped or twisted, this can usually be pressed out when clamping down. Note: if you notice planks like this use them for your smaller pieces if possible, that will minimize any inconveniences. Do a dry run, even figure out your clamping procedure and have the clamps prepared and ready to go. You might even need to make some clamping blocks or jigs to aid the process.
The standard carpenter's straight chisels are excellent for working on the flat wood surfaces during the attachment process. Also use guidelines or dowel location pins and be sure all of your internal doweling, if any, is prepared. External doweling, if needed, can be done later while it's still clamped-up or even after the clamps are off and the glue is dry. Screws can also be used if really needed, very rare, either remove them later after the glue is dry or counter sink them so that the heads are deep and out of the way, they can give your chisel a bad nick if you carve into one. Beware, with time, screwed areas will collect moisture and tend to rot first. Screws are not recommended.
The head and neck can be given slightly different positions, they are easily twisted or tilted for your animal's character at this time. This will give the animal an animated look rather than the in-line straight forward look. This is an area where you can be using the internal doweling. Usually, a carousel animal looks out a little bit to the right as they are being turned on the carousel in a counter-clockwise motion.
Additional part blocks
It is always good to pre-glue part blocks especially
when they are going to be used in a larger assembly, that way
you will have less slipping around. Small pre-assemblies are good to prepare. When doing stack laminations it is much easier to glue-up two layers at a time
rather than three or four, otherwise you have to deal with the bothersome slipping around of the pieces. Even though it might seem like it is taking extra time to do pre-assembly of part blocks, in the long run you save time and have a more accurate product.
Note: Occasionally you can do multiple stack gluing easily by lining
everything up, deciding on a couple of good locations for a guide dowel, then
drilling holes to create long channels for a couple of guide dowels, usually the
holes should be larger than the diameter of the dowel being used so that you can
actually get it through and any dripping around glue won't put a stop to it.
These dowels can be removed right after clamping or left in and just carved
through. Any holes or irregularities left by this process are easily
plugged.