It's possible with the internet to find, meet, and even marry beautiful Asian women. Though don't think that just because the internet is here that you can sit back and do nothing. There are very specific things you'll need to do if you want to attract a wonderful Asian woman to you.
Keep in mind that when you are talking about Asian women that can include many different countries, all with their own cultures and traditions. To really increase your chances of making a connection with someone you should narrow down your focus and concentrate on women from a particular country. It doesn't matter if it's Chinese, or Japanese, etc. Just pick one country and familiarize yourself with it's language and customs.
If you take the time to do this the women you meet will be very impressed and flattered that you took the time and effort, and those two things can take you a long way.
There are some general rules to keep in mind when dating Asian woman, though. For one thing, most Asian women will respond to a strong, assertive man. Please don't mistake this for a loud mouth, over compensating jackass. There is a huge difference and if you don't know what the difference is you better figure it out before you set out to meet someone otherwise you'll just turn her off and make a very bad impression.
Being strong and assertive means that you know what you want and you're not afraid to, politely, ask for it. Instead of some vague 'do you want to go out sometime?' try a more direct approach 'do you want to go to dinner on Saturday night'? That is a much better approach with most women, not just Asian ones.
Asian women aren't nearly as forgiving about appearance as American woman are. Today's American male dresses like they just rolled out of bed, they are often unshaven, wearing sloppy looking clothes that look dirty even if they've just been washed and usually need a haircut. While this scruffy look may work with American women, it won't get you anywhere with Asian women. They'd dismiss you as a slob quicker than you can say 'haircut'.
Asian women often are stereotyped as being gold diggers and calculating but that is very unfair. The truth is that their cultural upbringing has taught them that a man should be able to support his wife, and they naturally look for men who can do just that. It's a cultural thing more than anything so don't get freaked out if a woman you've recently met asks you some very personal questions about your health and finances.
Cultural differences not withstanding, beautiful Asian women are just like women, beautiful or not, everywhere - they want a man who will love them, respect them and treat them right. It's not rocket science and you don't need anything other than a little knowledge about the culture, some good manners and common sense. Using this approach will streamline the process of meeting the woman of your dreams.