My 230v 3 wire pump only has a red black and yellow wires no 4th wire green .
Do I need it if so where do I connect it to pump

Read the motor plate, what does it say ? Single phase or 3 phase? What is the voltage on the plate? What is the amperage? Are you describing the wire coming out of the motor or the wire coming in to the motor?

read the motor plate, what does it say ? single phase or 3 phase? what is the voltage on the plate? what is the amperage? are you describing the wire coming out of the motor or the wire coming in to the motor?

230volt single phase 3wire submersable well pump 3/4 hp all wiring diagrams show 4wires mine only has 3 red black yellow mine has no green wire.

Red and yellow is the start winding wire, black and yellow is the run winding, you need a pump control box for this pump, to switch from start to run mode.
You should have a ground wire from the well casing to the control box also

Here's a link to a diagram, page 8 looks like your setup

http://www.berkeleypumps.com/resources/images/2101.pdf

My casing is pvc can I hook a ground wire to one of the motor to pump mounting studs? Or should I just drive a ground rod for ground?

My casing is pvc can i hook a ground wire to one of the motor to pump mounting studs? or should i just drive a ground rod for ground?
Post the pump model number and manufacturer

post the pump model number and manufacturer

Franklin elect.1/3hp 230v 4.4amp 3wire pump motor model#2143034116 crane deming pump metal tag on pump reads 2xln-12-482

Looks like Franklin wants a 230v GFCI breaker feeding the well pump, the water column can become a ground path and possibly kill someone when a plastic drop pipe is used.
That part number does not search out on their site. Is this pump submersible or is this a motor bolted to a pump above ground? The part number looks more like that situation, in that case run a ground wire same size as motor conductors to the motor make up box and ground it there.
Here is the installation pamphlet from Franklin
http://www.franklin-electric.com/media/documents/M1311_60_Hz_AIM_Catalog.pdf
I copied this off page 9

The primary purpose of grounding the metal drop pipe
And/or metal well casing in an installation is safety. It is
Done to limit the voltage between nonelectrical (exposed
Metal) parts of the system and ground, thus minimizing
Dangerous shock hazards. Using wire at least the size of
The motor cable wires provides adequate current-carrying
Capability for any ground fault that might occur. It also
Provides a low resistance path to ground, ensuring that
The current to ground will be large enough to trip any
Overcurrent device designed to detect faults (such as a
Ground fault circuit interrupter, or GFCI).

An above ground surge arrestor must be grounded,
Metal to metal, all the way to the lowest draw down water
Strata for the surge arrestor to be effective. GROUNDING
THE ARRESTOR TO THE SUPPLY GROUND OR TO
A DRIVEN GROUND ROD PROVIDES LITTLE OR NO
SURGE PROTECTION FOR THE MOTOR.
To maximize delivery, are not recommended, since the
Suction created can be lower than atmospheric pressure.
%QUIPMENT 'ROUNDING
Primary path back to the power supply ground for any
Ground fault. There are conditions, however, where the
Ground wire connection could become compromised.
One such example would be the case where the water
In the well is abnormally corrosive or aggressive. In this
Example, a grounded metal drop pipe or casing would
Then become the primary path to ground. However,
The many installations that now use plastic drop pipes
And/or casings require further steps to be taken for
Safety purposes, so that the water column itself does not
Become the conductive path to ground.
When an installation has abnormally corrosive water
AND the drop pipe or casing is plastic, Franklin Electric
Recommends the use of a GFCI with a 10 mA set-point.
In this case, the motor ground wire should be routed
Through the current-sensing device along with the motor
Power leads. Wired this way, the GFCI will trip only when
A ground fault has occurred AND the motor ground wire
Is no longer functional.