If you've done any research into how to level up in your career, chances are good that you've heard how important it is to build up your emotional intelligence.

EQ is an in-demand skill that essentially refers to the ability to manage your own feelings and the feelings of those around you, which can make you better at building relationships and leading in the workplace.

Those with high EQ are excellent communicators and can leverage their empathy to gain people's trust. In a work setting, that can mean gaining influence as an effective leader who gets good work done and is a joy to work with.

Learning how to build your EQ skills is one big goal Christine Cruzvergara works on with her reports. Here's how she teaches them the skill.

How to practice your EQ skills at work

Cruzvergara, the chief education strategy officer at Handshake, has managed over 100 people in her career, and has learned to communicate well with CEOs and students alike. She recalls working with one report over four years to become more emotionally intelligent.

"She was aware of her own emotions, but she was really bad at reading other people's emotions," Cruzvergara tells CNBC Make It.

The report felt she was "always reading people wrong," and "because of that, she really struggled with figuring out politics within our environment and knowing how to navigate rooms and [know] who had influence."

One main strategy Cruzvergara and her report developed involved paying attention to the room dynamics in meetings.

After meetings with active discussions or possible disagreements, Cruzvergara would check in with her report to understand her takeaways. She'd ask questions like:

• What did you notice about everyone's body language, especially the leaders and their teams?
• Who seemed uncomfortable, and why? What cues made you think that?
• Did it look like the main speaker had already gotten buy-in before the meeting? What gave that away?
• What do you think is the core of the disagreement, and what unmet needs might each person have?
• Who appeared to have the most influence in the room? What signals suggested that?
• What does each stakeholder need to move forward?

Each person would share what they noticed and also discuss any discrepancies between what they took away from the interaction. This would help them "gather a fuller picture of the discussion and identify next steps" from the meetings, Cruzvergara says. As a result, the report "could start to train herself on the types of cues that she needed to be looking for" to interact well with others and gain influence at work.

Notice how people communicate

Another thing to pay attention to during meetings is how senior leaders speak up or present, Cruzvergara says.

Take note: Are they a succinct speaker, or do they really love context? Do people in the group tend to use data in the way they communicate? 

Observing how your company's VIPs communicate "tells you something about the way that they might like to consume information and what they care about," Cruzvergara says. Practice mirroring their communication style so you know how to best deliver information to them.

Overall, debriefing what happened during big meetings, and the aftermath of how it impacted the team, is one "example of how we took something that's really big ambiguous and broke it down into more tactical steps to actually help her improve on that particular skill set," Cruzvergara says.

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