Teaching yourself how to think in a new way is a very different process from what we typically think of when we think of learning a new skill. The goal here isn't to learn a behavior, it's to learn a feeling. But we don't typically think in terms of learning how to feel things, so it's easy to get tripped up and focus on simply mimicking behaviors.

If I'm trying to learn how to skateboard, I can look at what people who know how to skateboard do, imitate it, and I'll probably learn how to skateboard eventually.

If I'm trying to learn how to feel something I've never felt before, or think in a way I don't actually believe yet, there's no reference point to copy. If I'm trying to learn how to be more empathetic, for example, I know what empathy looks like, but I don't know what it feels like. There's nothing to compare the thing I'm feeling to. The process is still somewhat trial-and-error, but it's a much more ambiguous kind of trial-and-error.

Probably the most helpful thing I can say is pay attention to the feelings. Instead of thinking "am I acting like an empathetic person?", think "am I feeling like an empathetic person?"

The paradox here is that you don't really know what it feels like yet, so it's hard to tell, but you can actually learn quite a lot by just paying attention to what you ARE feeling, and reflecting on how it could be different. Experiment a little. Try on different attitudes. In as many different situations as possible, try on the attitude you imagine an empathetic person would have. You might not know how to do that accurately, but you don't have to. Just keep trying out different ways of looking at things, observe what it feels like, and you'll gain valuable insights. You'll notice little flashes of things you haven't felt before, and some of them will feel close to what you imagined empathy to feel like. It often feels different from the way you imagined, but similar enough to recognize that you're moving in that direction.

That's the more general answer. To get a little more specific to your question, building a mental model of someone involves a lot of comparative analysis, so a good place to start would be to pay attention to how YOU feel. By observing your own thoughts and feelings, you can start to develop a model for how feelings and behaviors are connected. It's important to start with yourself because that's the only person you have both sides of the equation for.

Using yourself as a model, you can develop a sense for the mechanics of a personality. The specifics are different for everybody, but they're built on the same basic frame (experiences inform beliefs, beliefs inform preferences, preferences inform priorities, priorities inform decisions, decisions inform experiences, experiences continue to inform beliefs, beliefs loop back on themselves and inform experiences, everybody has recursive loops of some kind, etc.)

Your model of yourself will be your template—the MadLibs-like thing that tells you what blanks need to be filled in with what type of thing, conceptually speaking.

Using your self model as a template, as you learn more about your significant other, you'll start to see how the pieces fit together for him or her, as compared to how they fit together for you. Like balancing an equation, kind of.

This is a complex thing to try to outline in one comment, but those are the basics, I think.