How to wire this AC fan?

Edited...

It appears to indicate the need for a start capacitor, that is more what the diagram you drew indicates or at least your drawing suggest what appears to be two windings...

 

The diagram is a little unusual but is clear. You have two wires coming in from the mains on the left. What is the problem?
The capacitor is 1microFarad 220VAC working and should be rated for continuous duty.

 

That is kinda what I got after further looking at it, but he said there was three wires coming from the motor, and that seems a little odd... I guess you can simply tag the green and red together outside the motor, but I would have thought that was done internally or at least on a common lug inside...

 

I would think that the capacitor is external to the motor as shown in the diagram.
With only 1uf, it is probably continuously connected, i.e. start and run.
The green and red wires should NOT be connected together, this would short one of the windings.

 

Depends on what side of the cap you are talking about, the diagram he drew shows the green and red common on the input side of the cap (unless that wire is red on that side of the cap), on the winding side it's a different story and yes would short... And this still brings me to the question of why there is three hookup wires, unless there is a lose of communication somewhere, and the green is not actually a hookup wire?

Edit and I think the lack of communication is whether the start/run capacitor is an integrated part of the motor or still needs to be supplied externally upon hookup...

 

Looks like a nice little fan.
An AC supply just goes up and down in voltage, it has no specific direction like DC.
To get an AC motor to rotate, two (or more) supplies are required with one supply running in front of the other. This gives a rotating magnetic field which the rotor follows. To get two phases, one supply is fed through a capacitor which advances the phase. Some motors switch out the capacitor when the motor is up to speed, this is capacitor start. Some retain the capacitor, like this one, as capacitor start and run. This saves a centrifugal switch.

Some small fan motors are shaded pole. The motor poles are split and a copper ring is placed around one half. This gives a phase retard to give the motor direction. These motors are uncased and so the innards can be seen and they are very inefficient so run hot.

 

First find your capacitor. It will need to be 1uF, the voltage rating must be for AC and could be higher than on the plate.
Second, decide how you wish to connect the wires. I would use a wiring junction box in the UK.
Connect the capacitor between green and red.
Connect the mains between yellow and red.
Switch on and duck!

If you are at all unsure about working with mains voltages, get some help. Be safe.