The term "Asian" is actually a very broad one, and encompasses several ethnic minorities from many different cultural backgrounds.
Taking the time to know a bit about the culture of the person you are interested in will prove invaluable in making an impression on them. Who are the famous or important people in their country? What's special or unique about their country's geography or history? What is the political or religious landscape like there? It is very important that you show some interest or investment in such matters; nothing will turn off a Korean girl faster than asking her if she's Japanese. Respect that traditions, attitudes, and ideologies vary greatly in different parts of the world. Listen, be enthusiastic, and put your best foot forward, and you will come across well.
If language is a barrier, the best way to get around it is to be polite and empathetic.
Probably she will be eager for a chance to practice her English. Many women from Asian cultures are looking for someone who will treat them well and who can demonstrate traditional attitudes, or at least an openness, toward marriage and family life. Women from Asian cultures will often have different interests and a different sense of pop culture norms. Be open to the sort of music they like. Be open to what their idea of a fun date is. Be aware that they might prefer certain kinds of food. The better you can listen to them, the better you can respond to their expectations. Be aware that women from Asian cultures will often respond strongly in positive or negative fashion to racially-determined physical characteristics. Tall, blonde-haired, blue-eyed men will have an easy time of it while living overseas. That said, everyone responds a bit differently, and you might be surprised by the things different women find attractive about you.
Men from Asian cultures as a rule are driven by the welfare of their family, and this is especially true of the first-born or eldest sons of a given family.
They are not all strict traditionalists, but they are very likely deeply aware of things like personal integrity, social hierarchy, the appearance of propriety, as well as a sense of duty and a desire for harmony. They may see romantic and physical love as two separate things. Accept gifts, give him a chance to act chivalrously, and show appreciation for his attempts to impress you. Getting him talking about his mother will give you good insight into what sort of lover he is.
Finding a Date
Many online services offer to introduce you to Asian people for dating or friendship purposes.
Barring that, one can often get to know Asian people by spending time in the same places they do. Most university campuses will have some popular restaurants frequented by Asian students somewhere nearby. Taking a language course is a great way to get connected with an Asian community locally. If you have a college degree, consider spending a year teaching overseas. Many academies in Asian countries hire foreigners, the pay is often good, and there is no better way to meet Asian people than to spend a year living in Asia.