I cut my animal shapes using a Cricut, but you could freehand them or trace figures or shapes.
To assemble the mobile, I tied everything together with white thread. Working from the bottom bar up, I adjusted the spacing between the animals until the bar was balanced. To keep them in place, I put a drop of glue over the knots on the skewers. I also glued the threads going between skewers.
On the upper two bars I didn't want to add a second animal to balance the first, so I tied glass beads onto the skewers with the thread.