What does "until fork tender and the juices run clear" mean and how do I tell?
It is a "metric" which requires experience to recognize. 

First, juices "running" clear doesn't mean that they will flow freely. You have to cut into the meat and look at the juice inside it. Is it clear or not? 

Second, there is a difference between the feel of meat at different stages of doneness, when you poke it with a fork. If you cannot notice it, this means you haven't trained yourself sufficiently. Noticing the difference is a skill which has to be learned. 

As you can see from the other question and the comments, the thermometer is the recommended way to do it. The old thermometerless way is both inaccurate and has a learning curve, making it hard for people to learn cooking. In fact, it is not really a metric. Experienced cooks recognize meat which is done by look and feel, including a look on the inside (cooking) and feeling with a fork instead of burning their fingers. What the recipe really says is "stop cooking when it's done". But because this sounds like a tautology to inexperienced cooks, the experienced ones try to describe in words what they should be looking for. And so this rough description is created, and the inexperienced ones use it as a guideline while learning to recognize doneness by trial and error. 

Of course, it is always good to pay attention to your meat when you are cooking it. Do look at the state of the juices and the feel when poked with a fork, and you'll learn to recognize it with time. But before you have become comfortable with your knowledge that the meat is done, rely on the thermometer instead of the feeling. Also, if you want to comply with food safety rules, you have to use the thermometer every time, as meat cooked by feel is not guaranteed to have reached the recommended temperature and will be sometimes unsafe.