How do I wire up this 4 wire 120v AC motor and capacitor
Pretty much all AC motors which use capacitor and have no centrifugial switch  require one winding connected directly to the outlet while another is connected via capacitor. 

Here is a diagram (I am not sure if your motor is actually PSC, but the schematics is the same as for the other motor types):
http://www.simplecircuitdiagram.com/2010/11/18/permanent-split-capacitor-capacitor-run-ac-induction-motor/

Use an ohmmeter to find out where the windings are. There should be &lt;100 ohms between wires corresponding to the same windings (likely only few ohms) and >1M ohm between wires which correspond to different windings. 

Label wires for one winding as A1 and A2, and wires for the other winding B1 abd B2. Then:


A1 and B1 are connected together and go to neutral wire.
A2 goes to live wire.
B2 goes to a capacitor; the other lug of the capacitor goes to live wire.


In case of wiring errors or unusual motor types, have fire extinguisher ready when turning the motor for the first time and be ready to unplug the motor if it hums instead of turning. Or connect a 100W lightbulb in series with it.