I am installing a subpanel on a wall that has drywall on it. I was planing on
Buying a plywood and installing my subpanel on the plywood, then attach
The plywood to the wall.

What size thickness does the plywood needs to be for mounting a 20 circuits subpanel on it?

Assuming the answer is minimum of 1/2 inch, then another question is,
How long and how thick would the screws need to be ? If it's 1/2 inch plywood,
It doesn't sound enough for holding the panel. What is the practical answer.

Also, when mounting the subpanel on the plywood, how much plywood should show on
The four sides of the subpanel?

There is no real minimum as far as I know. Commercial installs use Unistrut or metal lumber.

It would seem resonable that you would need to access a stud which is normally 16" on center. So about 18" would be about right.

Using a typical screw designed for wood about 1-1/4" long would be fine.

Your choice as to how big the plywood should be.

In fact, if you wanted, you could use two pained or stained piece of 1/2 x 3 and just use two strips to span a stud and mount it off the wall.

Plywood is just "not pretty".

Thanks KISS, you seem to always have great answers for me. Thanks again.
I just checked out Unistrut videos from their site. That is an amazing, but yet simple
To use product.
I hear finding a dealer that sells it to DIY'ers is difficult. Any online store you would recommend that would sell to residential customers?

Any electrical supply house has a limited number of parts available. The generic term is "strut systems".

Some online retailers are:

General Fasteners: Barnhill Bolt Co., Inc. (http://shopping.barnhillbolt.com/index.asp?file=STRUT.htm)

And

Industrial Supply Equipment from MSC Industrial Supply (http://www.mscdirect.com)

I just happen to have an MSC store about 2 miles from me.
If I can wait for a product (1-2 weeks), I can have it shipped there with no postage.

Pay attention to size. Width is pretty constant, but height can change and so can fastener capability. For instance, the pipe clamps won't fit in the (5/8?) channel.

Unistrut likes coming in green, but most may be galvanized which is impossible to paint.