Courtesy

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Most Japanese people will understand that you are a foreigner and not expect a strictly correct introduction from you, and will likely try to shake your hand (because that's the cool American way to do it), but if you want to be as culturally appropriate as possible, read on.
When you don't know someone, it is generally accepted that you shouldnt look them in the eyes for more than a brief glance. This sort of behavior will get you many stares when on the train or in other public locations. When you meet someone in a situation where you should give them your name, then you should start with hello (こんにちは) then introduce yourself (私はラセルです), and then wait for a pause to see if they will tell you their name. If they do, great. If not, you can ask for it (あなたのお名前は何ですか。) They will then tell you their name. After that, there will be an exchange of "good to meet you, please treat me nice" (どうぞよろしくおねがいします。)　At this point, (or whenever your partner bows) you should bow from your waist. If you are female, place your hands flat on the front of your thighs, if you are male, your hands should be at the sides of your legs. Make sure that you don't look at the floor while you bow, but rather at the person you are bowing to.
If business cards are involved, hand and recieve them with two hands while bowing. Make sure that you give yours in such a way that your partner doesn't have to turn it over to read it.

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礼儀