If you have had any experience of working or meeting Japanese people, you will have noticed that they often bow and say to you Yoroshiku onegai shimasu. The expression Yoroshiku onegai shimasu is not only used in introducing yourself but when you are asking someone a favor.
For example, Yoroshiku onegai shimasu is sometimes found at the end of an e-mail or a letter. You might have wondered what favor the person who wrote it was asking. Well, it may not refer to anything in particular, but saying Yoroshiku onegai shimasu is a general greeting covering the whole content of the e-mail or a letter. You could say this is one of the typical Japanese expressions. And what do you reply if someone says Yoroshiku onegai shimasu to you? Just repeat it—Yoroshiku onegai shimasu!