One of the best ways to learn quickly is to visit them in their space - their apartment or house. Ask if you can come over, and set a time with them. Put aside your hesitations that stem from your American upbringing - they do not see this as an invasion of privacy or an intrusion of their space. In fact, in every situation I've experienced, they love this!
Try to plan this time when you don't have an important appointment afterward... Again, don't have an American mindset: "Dinner with my international friends at 5:00, piano recital at 7:00." Chances are, if you arrive at 5:00, they may begin preparing the meal around 5:30, and you may not eat until around 7:00! To avoid feeling stressed, do not have an agenda. If you must leave by a certain time, make sure to let the host know, when you make plans with them: "My daughter has a piano recital at 7, so I'm sorry but it is very important that I leave your house at 6:30." Read a personal story about being time-conscientious.
It is a good idea to take a small, modest gift for the host, to thank them for their hospitality - flowers, a sweet treat, or something you made... or it could be something to say, "Welcome to America," like a good family friendly movie or a local souvenir.
When you enter their space, keep in mind that you are the foreigner. Do not expect their home to look or sound or smell like yours! The meals may be served on the floor, the thermostat may be set at 80 degrees, and the windows may be covered with big pieces of colorful material. Even though this house may be built in downtown USA, the minute you step through the door you might find yourself in a different country. And that is not only ok, it is beautiful and exciting and adventurous for you! This is where your international friend is in their element - this is their comfort zone and safe haven, where they know the rules and can relax in their own skin.
Because you are the foreigner, submit yourself to the role of learner. Pay close attention to everything! What do you see? Is there a pile of shoes in the entry? If so, take off your shoes too. Where and how are people sitting? Try to sit on a lower level than the oldest person in the room, unless they insist that you have a "seat of honor." What do the decorations tell you about what is valued? Ask questions, if you see something interesting or unusual; point, and say simple words like, "your home country?" or "you make this?"
Inevitably, you will be offered or given something... A bottle of water, a can of pop, a plate of cookies, or a full-blown meal. Take it! If they made a meal and want you to eat, eat it! Unless you have an allergy or legitimate dietary issue, I recommend that you not ask "What is it?" before the meal... sometimes we enjoy things more in ignorance. Read this fun story about a special eating experience I had. If you are sensitive to spicy things, eat small portions slowly, and eat more rice or bread. But please make an effort to try everything that is put in front of you. With that in mind, forget what your mother said about cleaning your plate! If you finish everything on your plate, your host is likely to continue to fill it indefinitely. They want to make sure that you know they have enough food to satisfy you. It is better to leave a little bit on your plate to signify that you are full and don't want any more.
Eating with an international family is an excellent opportunity to learn from them. Do they sit on the ground? at a low table? with their hands? with chopsticks? from a common bowl? using bread to scoop? Take this time to observe, ask a lot of questions, and imitate what you see. Let them correct you, demonstrate for you, and give you guidance. This is an honor for your international friends, to teach you something new.
After the meal, pay attention - who is cleaning up? Ask how you can help. What is everyone doing? Stay and watch the World Cup, or help the kids with homework, or listen to a story, if you can. When it is time for you to leave, thank and say goodbye to each person. If you feel comfortable, you may even ask if you can pray for God to bless the family before you go - blessings are rarely turned down! You may be completely exhausted and overwhelmed when you leave, but know that you have made significant steps in building bridges and tearing down barriers. You've had a cross-cultural experience that was authentic and intentional!