Personal information

When Japanese meet someone for the first time it is common for them to reffer to themselves with their last name and the respectful "san" title. This is important!
(last name) desu. / (last name) to moshimasu (humble). = My name is (last name).
Personal information
Dochira kara, irasshaimashita ka. = Where are you from?
Kanada kara kimashita. = I am from Canada.
Okuni wa dochira desu ka. = Which country are you from?
Oumare wa dochira desu ka. = Where were you born?
Roma de umaremashita. = I was born in Rome.
Osumai wa dochira desu ka. = Where do you live?
Kanada desu. = I live in Canada.
Kakkon shite irasshaimasu ka. = Are you married?
Kekkon shite imasu. = I am married.
Dokushin desu. = I'm single.
Okosan ga irasshaimasu ka. = Do you have any children?
Oikutsu desu ka. = How old are you? (Another way of saying what I taught you a long time ago.)
Oshigoto wa. = What do you do?
Gakusei desu. = I am a student.
Kyoshi = teacher
Kyoju = professor
Shufu = housewife
Kaishain = office worker
Sarariman = office worker (for men only)
Hisho = secretary
Gijutsusha = engineer
Gunjin = in the military
Kaisha no shacho = company president
Kaisha no juyaku = company executive
Jitsugyoka = industrialist
Isha = doctor
Haisha = dentist
Kangofu = nurse
Yakuzaishi = pharmacist
Bengoshi = lawyer
Kaikeishi = accountant
Kenchikuka = architect
Ongakuka = musician
Geijutsuka = artist
Sakka = writer
Seijika = politician
Yakunin = government official
Komuin = government office worker
Janarisuto = jounalist
There's a nice list of professions for you! Sakka desu. I hope your day goes amazingly and maybe this will someday come in handy if you ever find yourself in Japan for some unknown reason and need to express the fact that you work in an office. Oh! One more thing I feel is necessary to say is: Disuko de, odoritai no desu ga! (I feel like dancing in a disco!)

Introductions

Japanese culture is something that they don't expect foreigners to ever fully understand, there are some things, however, which we can try and grasp. "Proper" intruductions are very important in their culture and although you can introduce yourself and will probably strike a fantasic conversation, it is better if a mutual friend or aquaintance does this with you.
Introducing yourself/Introductions
Ano kata wa, donata desu ka. = Who is that?
Ano kata ga donata ka, gozonji desu ka. = Do you know who that is?
Ano kata ni, aitai no desu ga. = I would like to meet him/her (literally, that person).
Ano kata ni shokai shite itadakemasu ka. = Would you introduce me to him/her (that person)?
A san, B san o goshokai shitai no desu ga. = Mr./Ms. A, may I introduce Mr./Ms. B?
Koko ni iru no wa, watakushi no _______ desu. = This is my _______.
Yujin = friend
Otto/Shujin = husband
Tsuma/Kanai = wife
Musuko = son
Musume = daughter
Chichi = father
Haha = mother
Hajimemashite. / Dozo yoroshiku. = How do you do?
Hajimemashite. / Kochira koso yoroshiku. = How do you do (reply).
Ome ni kakarete, koei desu. = I'm honored to meet you.
Ome ni kakarete, ureshii desu. = I'm glad to meet you.
Your name to moshimasu. = I'm your name.
Watakushi no namae wa, your name desu. = My name is your name.
I know that some of them are different ways of saying the same thing but I figure that you may make use of all of these phrases at some point or another. I hope you go and introduce yourself--or have someone else introduce you--to a new Japanese friend!

Days of the week, Months of the year

I'll find out when these are due... procrastination is a very real thing. Fortunately I get over it sometimes and get my work done on time!
Days of the week
In English we have Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. The naming system is based off of the planets in our solar system, our "moon" and the sun itself:
Monday(Moon), Tuesday(Mars), Wednesday(Mercury), Thursday(Jupiter), Friday(Venus), Saturday(Saturn) and Sunday(Sun).
In the Japanese language, the days of the week are not based off of the--excluding Saturn--planets, though it does have moon and sun. Really, it is not all that different than ours, only in another language, in Japanese. The elements play a large role in the naming of the Japanese days of the week.
The word we use in English as "day" is similar to how they use "yobi".
Moon yobi
Fire yobi
Water yobi
Wood yobi
Gold yobi
Saturn yobi
Sun yobi 
In Japanese these words are:
Getsuyobi=Monday
Kayobi=Tuesday
Suiyobi=Wednesday
Mokuyobi=Thursday
Kinyobi=Friday
Doyobi=Saturday
Nichiyobi=Sunday
Months of the year
In Japanese, the months are defined by their number. January is the first month and is therefore the "first month" or "month one". Some of these numbers may be familiar to you if you have read the numbers entries. Some of the numbers are abbreviated for the months so keep that in mind if you become confused. "Ku is not a number!" No, but kyuu is.
Gatsu=month
Ichigatsu=January
Nigatsu=February
Sangatsu=March
Shigatsu=April
Gogatsu=May
Rokugatsu=June
Shichigatsu=July
Hachigatsu=August
Kugatsu=September
Juugatsu=October
Juuichigatsu=November
Juunigatsu=December
So, for example, November is "The eleventh month", as March is "The third month"
Relative months
Sengetsu=last month
Kongetsu=this month
Raigetsu=next month
Relative days
Ototoi=the day before yesterday
Kinou=yesterday
Kyou=today
Asu=tomorrow
Asatte=the day after tomorrow
Relative weeks
Shu=week
Senshu=last week
Konshu=this week
Raishu=next month
Reletive years
Kyonen=last year
Kotoshi=this year
Rainen=next year