Creating a gently moving 2D fog effect
Animated noise can be created by using time as an extra dimension. So instead of 2D noise, you'd use 3D noise with time as the z-axis position, like ofNoise(x, y, time).

To control the level of detail, you'd use octaves of noise: multiple noise layers with different scales and amplitudes, mixed together. The basic Perlin routines just generate a single octave, so you can re-invoke it with scaled coordinates to add more detail, something like:

float noise = ofNoise(x, y, time);          // first octave
noise += 0.5 * ofNoise(2*x, 2*y, 2*time);   // second octave
noise += 0.25 * ofNoise(4*x, 4*y, 4*time);  // third octave


and so on. The more octaves you put in, the more detailed the noise will be. The article you linked describes this in more detail if you scroll down to Working with Octaves.