Well, there are both physical and psychological signs. You’ll likely be irritable, restless and have trouble falling asleep. In training, you can’t focus, and feel fatigued or sluggish. In short, you feel like crap.
Try to incorporate compulsory rest periods in your training calendar. Also, vary your activities, especially after a focused period of training for a race. For instance, I take up inline skating and yoga during my off-season.