How do pilots avoid clouds under night VFR?
I will caveat my answer by saying that most of my night flying has been under IFR, but because of that I have lots of experience going in and out of clouds at night.    

It starts with a good weather brief, and don’t forget to ask for PIREPS that might cover areas further away from the field.  True enough the bases can be ragged, and little puffies can lurk in unexpected places, but if you know where the layers are called you are well on your way to avoiding being at the same altitude.  

To add to one of the comments, moonlight is helpful, but so is ground lighting.  At night distant clouds can be difficult to see, but you can use ground lighting to gauge where the coverage is.  For example, if your eyes can trace a lighted road off in the distance, but at approximately 20 degrees below the horizon the car lights become blurry, then disappear, it is probably because of a cloud between you!  Angle away, or descend below the deck until the horizontal visibility range increases.

If you start skimming clouds you will know it immediately because your anti-collision light will blossom and reflect red all over the inside of the cockpit.  If you still have ground lights in sight and you know the clouds are stratified, I would start a gentle descent.  If there are a lot of vertical buildups and you pop into one and lose sight of the ground, make a level 180 and get out of there.  Most non-instrument rated pilots are taught to deal with inadvertent IMC in this way.

As I mentioned in my answer to your other question, make sound risk decisions.  If you are uncomfortable with the weather conditions or your ability to remain clear of clouds, then choose to not fly VFR at night.  But once you get a few night flights under your belt I think you will find that they can be very enjoyable when conditions are good.  It opens up a whole new perspective on things!