What is the resistance of a typical PCB?
The resistance between any two points is infinite.

In the real world, you can't make a true point contact.  It will always have some diameter or other finite dimensions.  Those dimensions relative to the separation distance are required to determine the resistance between, given the resistivity of the material.

Let's say your "points" really have 1 mm edges facing each other, and that the separation is also 1 mm.  Consider how the resistance would change if those edges were instead 1/2 mm.  You can think of the original set of points of being made up of two of these smaller ones in parallel.  This means the resistance between the 1/2 mm edges would be twice that as between the 1 mm edges, all else being held the same.

Now consider what happes when you move the original 1 mm points farther apart, to 2 mm.  You can now think of this new configuration as being two of the previous in series, so must have twice the resistance as the original.

The relative geometry matters.  Hopefully you can see by now that as the "points" are shrunk smaller and smaller, the resistance goes up.  When they become infinitely small true points, the resistance is infinite.

So how do you quantify all this?  Consider doubling everything about the original configuration so that you now have 2 mm edges separated by 2 mm.  Each 1 mm slice looks like two of the original in series, so twice the resistance.  However, you have two of these slices in parallel, so that doubled resistance is halved again, getting you back to the original value.  In fact, for uniform surface conductivity on a infinite plane (or close enough, a PC board much larger that the dimensions of your test area), the resistance stays the same when all the linear dimensions are scaled uniformly.

This is why surface resistivity is usually quoted in Ohms per square.  That would be two 1 mm edges separated by 1 mm, two 7.3 mm edges separated by 7.3 mm, etc.  As long as you measure the resistance between opposite sides of a square, you will get the same answer regardless of the size of that square.

Well made and clean PC boards can have surface resistivity in the 10s of G&Omega; per square.  It goes down from there with moisture, accumulated dirt, and poor PCB fab processes that leave ions on the surface or in the mix.  Solder mask helps with this for traces that can be covered, but surface dirt accumulation will be a long term problem for anything not covered.  This is the main reason for large creapage distance requirements where even small leakage currents can be a problem, like in patient-touching medical equipment.