This tutorial has some good tips on casting wax. Wax casting resembles silicone casting in a lot of ways, except the wax hardens as soon as it gets cold. If your mold is super cold, the wax can trap little bubbles against the surface and they'll end up as voids in your final wax part. Wax is also a pretty good insulator. It takes longer than you'd figure for your parts to fully cool so don't rush to pop them out of the mold even if the surface is lukewarm. Wait about an hour before demolding and assembling the core.
To make sure everything was aligned I cut myself an alignment jig out of acrylic. This isn't completely necessary if you're careful and keep the core straight as you put it together.
To assemble the core, fit all the pieces together and go around the seams between the ribs and the base with a hot soldering iron. If you're worried about wrecking your iron's tip, use a piece of wire wrapped tightly in foil as a replacement iron tip/wax knife. You might end up needing to add a bit of wax to the seams, so use some of the spare wax from your casting like you'd use solder and fill in wherever necessary.