In their book Emotional Intelligence 2.0 Travis Bradberry and Jean Greaves have explained how to feel emotions physically.
When you experience an emotion, electric signals course through your brain and trigger physical sensations in your body. The physical sensations can be varied as your stomach muscles tightening, your heart rate increasing your breathing quickening, or your mouth going dry. Because your mind and body are so tightly connected, one of the most effective ways to understand your emotions as they are happening is to learn how to spot the physical changes that accompany your emotions.
To better understand the physical effects of your emotions, try closing your eyes the next time you have a few moments alone. Feel how fast or slow your heart is beating. Notice the pace of your breathing. Determine how tense of relaxed the muscles are in your arms, legs, neck, and back. Now, think of a couple of events from your life - one positive and one negative - that generate strong emotions. Think through one of these events in enough detail that you can feel your emotions stir. Take note of the physical changes that accompany the feelings. Do they make your breathing or heart rate change? Do your muscles grow tense? Do you feel hotter or colder? repeat this process with the other event and take note of the physical differences in the emotions from the positive and negative experiences.
Closing your eyes and thinking of emotionally arousing events is simply training for the real thing- spotting the physical science of your emotions on the fly. In the beginning, try not to think too hard - simply open your to noticing the sensations. As you improve at this, you will find that you are often physically aware of an emotion long before you are mentally aware of it.