How to create one object for multiple uses the right way?

While I was working on a class which required random number generation, I was thinking about a way to create just one Random object for multiple uses.

I read about static factories in effective java and came up with this, but the more I think about, the less logic I see in this. Is this the best way? And does this make sure only one Random object gets created?

public static Random newInstance() {
    return new Random();
}

public static void generateRandom() {
    Random rand = newInstance();
    //...
}

Another way is initialising it in the constructor, although I'm not sure if this is the best practice?

public static Random rand = new Random();