As soon as you and your teacher finish saying hello to each other 37 times, the next phrase that's likely to pop up is はじめまして ( hajimemashite). There's no really good equivalent for this in English. Technically it means something like “I am meeting you for the first time (初め / hajime means “first time). If you look at a Japanese-English dictionary, then it will say something like “Nice to meet you." I suspect that this is the culprit behind Japanese people's obsession with saying “Nice to meet you" in English before they even know your name.

This is the usual flow of a first-time meeting in Japanese (in a formal setting):

Let's look at this conversation in a bit more depth…

Like I said earlier, this just means “I'm meeting you for the first time." The reason that I don't include こんにちは ( konnichiwa) in this section is that you don't necessarily need to say it before はじめまして (hajimemashite). It's okay if you do, but it's not required. That's why I translated this as “Hello (for the first time ever)."

です ( desu) is kind of like English's “to be" verb, and in much the same way, it can be used to say about a million things. The simplest construct is the one we see here:

[Noun] + です = …is noun.

Notice anything strange about that sentence? I haven't written a subject for either one. You could think of this sentence as having an unspoken subject, which a lot of textbooks will say is 私は ( watashi wa).

私 ( watashi) means “I." and は (wa) is a topic-marking particle (don't worry about it). If I wanted to include “I," which is totally unnecessary, I could say:

私(わたし)はニコ(にこ)です。
watashi wa Niko desu.
I am Niko.

A lot of people, in explaining the first-time greetings written above, will write something like this:

（ 私(わたし)は）ニコ(にこ)です。
(watashi wa) Niko desu.
(I) am Niko.

That's probably a totally sufficient explanation. However, if you're going to get technical about what is and is not the subject of this sentence, things could get pretty complicated. If you're an intermediate student or above, Jay Rubin's Making Sense of Japanese has a very interesting explanation of this, in which he talks about “the zero pronoun" of Japanese.

If you're at a Japanese school, they will probably press you to say 私 ( watashi), and I guess it is technically more polite. Personally, I try to avoid saying “I" whenever possible in Japanese, and I think that as a result I've developed an aversion for the word 私 (or any of the many other forms of self-address in Japanese). Say it if you want. But you're not incorrect by not saying it… and that sounds easier to me.

The word お願い ( onegai) means “favor." So if you add the verb する (suru) to it, which in this case is conjugated to します (shimasu), “to do," then you get “do a favor." This is one of the many ways to say “please" in Japanese.

宜しく ( yoroshiku), however, is a much less easily defined word in English. I've seen it translated into all of these things:

• best regards
• please remember me
• please treat me favorably
• please take care of
• I'm counting on you

Generally speaking, my sense of よろしく ( yoroshiku) is that it means something like “Please be nice to me" or “Please do [nice thing] for me."

So if we add all of this together, we get: “Please be nice to me please." Beautiful English, right? Because of its contextual use, however, it gets translated to become “Nice to meet you." I guess the nuance is something like, “Let's have a good relationship from here on out."