Making a Point Class in Python

Dont forget math.hypot

def distance(self, p):
    dx = self.X - p.X
    dy = self.Y - p.Y
    return hypot(dx, dy)

You declared distance as taking an argument p; inside the method youre referring to it as other. Change p to other in the declaration so they match.
sqrt() isnt a builtin; you need to do import math and refer to it as math.sqrt().
You arent doing anything with the testPoint() function you declare; you can invoke it by adding a line at the end like:

print distance = %s%(testPoint())

At that point, your code works and computes a distance of 4.0 between your points.

Now, some style issues:

In Python, you dont generally privatize member variables, and you dont bother writing trivial getters and setters, so you can remove the getX() and getY() methods and just refer to p.X and p.Y directly given a Point p.
The math module has a convenient hypotenuse function, so in distance() you can change the return line to return math.hypot(dx,dy).
By default, a user defined object has an unattractive string representation:

<__main__.Point object at 0x1004e4550>

You should define a string conversion method in your class like so:

    def __str__(self):
        return Point(%s,%s)%(self.X,self.Y)

This will be used when the object is printed, or otherwise needs to be converted to a string.

In your Point.distance method, you reference other.X and other.Y; Other does not exists.

You should either change the distance signature to be distance(self, other) or change the code to use p.

You will also need to import math.sqrt:

from math import sqrt