Humans are generally pretty well-equipped to model other people, and you can practice using that equipment. Imagine as vividly as possible what it would be like to be the other person. Be aware of your own past feelings and other mental processes, in such a way that you can access those memories when you notice that the other person might be experiencing something which is (on some axis) familiar to you. Keeping a journal can help with that. It's also useful take some time to think of your own ways to practice this, where 'practice' includes getting and incorporating feedback. As Qiaochu points out you can be empirical. I would add that 'testing hypotheses' includes asking people about their internal state.

If you know anyone who seems to 'get people' especially well, ask them how they do their thing.

Look for existing resources on building empathy skills.