What is the best way to implement constants in Java?

That is perfectly acceptable, probably even the standard.

(public/private) static final TYPE NAME = VALUE;

where TYPE is the type, NAME is the name in all caps with underscores for spaces, and VALUE is the constant value;

I highly recommend NOT putting your constants in their own classes or interfaces.

As a side note: Variables that are declared final and are mutable can still be changed; however, the variable can never point at a different object.

For example:

public static final Point ORIGIN = new Point(0,0);

public static void main(String[] args){

    ORIGIN.x = 3;

}

That is legal and ORIGIN would then be a point at (3, 0).