(inspired by Stephen P. Robbins' book titled Organizational Behavior)

Understanding another person's felt emotions is a very difficult task. But we can learn to read their displayed emotions.
We do this by focusing on verbal, nonverbal, and paralinguistics cues.

The easiest way to find out what someone is feeling is to ask them.(I know it seems that I'm only stating the obvious, but bear with me on this and read on ((-: )
Saying something as simple as "Are you OK? What's the problem?" can frequently provide you with the information to assess a person's emotional state.
But relying on a verbal response has two (2) drawbacks:

1. Almost all of us hide our emotions to some extent for privacy and to reflect social expectations. So we might be unwilling to share our true feelings.
2. Even if we want to verbally convey our feelings, we may be unable to do so. Some people have difficulty understanding their own emotions, let alone be able to verbally express them.

Therefore, at best, verbal responses provide only partial information.

Say you were talking to a co-worker, when his/her back is rigid, teeth clenched, and facial muscles tight tell you anything about his/her emotional state? It should.
Facial expressions, gestures, body movements, and physical distance are nonverbal cues that can provide additional insights into what a person is feeling.
Even something as subtle as the distance someone chooses to position himself or herself from you can convey their feelings, or lack thereof, of intimacy, aggressiveness, dislike, or withdrawal.

The third source of information to a person's feelings is paralanguage. This is communication that goes beyond the spoken words, which includes pitch, amplitude, rate, and voice quality of speech. Like the saying goes "it's not just what you say, but how you say it".

So the next time you are communicating with a colleague, a peer, or even your boss, as you pay closer attention to what they are saying through all of the three cues...you will be able to more accurately assess the emotions being communicated.

Good luck!