Basically, trigger points are overstimulated areas or "knots" in the fascia. They keep the muscles from fully relaxing and pull everything out of alignment. Often they'll refer pain to other areas. Fascia connect muscle to tendon, which is why trigger points are often involved in tendinitis.

You can often feel them externally as lumps in the muscle, especially when you go deep. You can definitely feel pain when you press on them! The simplest way is to roll out the whole muscle group and give extra attention to the trigger points as you find them. A spiky ball is especially useful for places with a lot of small muscles like the hands and feet, but NbyNW is right, a tennis ball or golf ball is good for the arms, chest and shoulders; for large muscles like the IT band area, a foam roller or larger ball.