If you don't have a heart rate monitor, there are other ways to monitor your exercise intensity. One of those is the Talk Test, which is just what it sounds like--the ability to talk during your workout can help you determine how hard you're working. The
American College of Sports Medicine states: "People who are able to comfortably converse during exercise are likely working out at an acceptable intensity." If you can speak comfortably, you're probably somewhere around the low-middle range of your THR zone (or a level 4-5 on the Perceived Exertion Scale).
Experts generally suggest that you shouldn't be breathless during your workouts. However, if you're doing interval training or a short, high intensity workout, being somewhat breathless is what you're looking for. Obviously, if you feel dizzy or lightheaded, you should slow down or stop exercising.