The bottom of the air pump has two solder connection points. One is marked with a red dot -- this is the + side. Solder a red wire to this point and a black to the other. 

Make these wires pretty long. The photo shows shorter wires, but ultimately I ended up lengthening them to around 2-3 feet, roughly the same length as my silicone tube. This pump is a bit noisy so longer wires will give you more options for hiding / quieting your pump so as not to ruin your illusion with mechanical noise.

Connect the red wire to the + terminal on the MOSFET and the black to the - terminal.

Use a screwdriver or your finger to gently press the tabs on top of the terminal. Insert about 1/4" of stripped wire and release the tab. The wire should stay connected tight when you tug on it gently.

Plug your STEMMA cable in to the MOSFET. Solder the three wires to the Circuit Playground Express as shown: Red to VOUT, black to G, and white to A1.

I kept these wires pretty short. The Circuit Playground Express and MOSFET will both be attached to the bottom of the jar, so I tried to minimize additional wire here.

That's it for the electronics! The silicone tube will attach to the opening on the top of the pump, where the air flows out. The opening on the side of the pump is the air intake, so be sure not to block this hole.