You must first determine your level of knowledge about the values, practices, and experiences of individuals who are culturally different from you. Find a culture that has always seemed interesting to you. For instance, if you were to choose Hispanic cultures you could learn about Hispanic food, language, and customs. Develop a special interest in language and foods from Hispanic cultures. Take the opportunity to talk with people from cultures different than yours but take heed to be respectful at all times during these conversations. You could also study the history of the culture that you are interested in, one suggestion though in order to understand a culture you must study their perspective of historical, and recent events. Accept any opportunity that you can to learn about cultures different from yours.
Your attitudes and perceptions are influenced by your world view, which is also influenced by your racial and ethnic identity, gender, and cultural experiences. Your experiences, culture, and identities influence what you say and how you interact with people from a culture different from your own. So the best thing is to educate yourself about cultures that differ from yours.
You also need to evaluate your strengths and weaknesses when interacting with culturally different individuals. Try asking yourself these questions: Do you try to understand people for who they are or do you judge them by what they look like? Do you form opinions about people without knowing anything about the personality of the individual? Do you understand the social cultural norms of others? What biases, perceptions, attitudes, and beliefs might you hold about culturally different groups? Once you are able to answer these questions you should have a good idea of where you need work and where you excel. The most important thing about increasing you multicultural intelligence is to develop an open mind, and understanding of cultures different from yours. You do not need anyone to guide you through this process you simply pick a culture and study various aspects of it.
American Psychological Association (2003). Guidelines on multicultural education, training, research, practice, and organizational change for Psychologists. American Psychologist, 58(5), 377-402. doi:10.1037/0003-066X.58.5.377.