Sumimasen ("excuse me, sorry") is a very useful word for any gaijin (outsider) negotiating Japanese public transport. Onegaishimasu "oh-nee-gai-shi-mas-(u)" means "please". "Arigatou gozaimasu" means "thank you".
Meal time is a great opportunity to impress. Itadakimasu is heaps of fun to sing out before dinner "ita-daki-mas-(u)!" - it means, roughly, thank you for giving me life. Sometimes it sounds like Japanese speakers are leaving out the "ooh/u" sound in desu, masu, etc, but it is there, it is just hard to hear. "Gochisoosama deshita" ("thank you for the feast"). "Go-chi-soo-sama" on its own is less polite, but means delicious. Your hosts will not mind if you forget your deshita. "Oishii" means yum and "kanpai" means "cheers"!
When entering any shop at least one voice, if not a chorus, will enthusiastically call out "Irasshaimase!". Responding to this with "arigatou gozaimasu" is like responding to a market vendor saying "Come closer, come closer!" with "Thank you! Thank you!". A little bow or a smile is fine. Also handy is "i-ku-ra-des(u)-ka?" ("how much is it?").
I have a few more. Hai rhymes with kai and means "yes", iie "e-aye" is "no". Eigo "ee-go" is the Japanese word for English. "Mizu" is water, "toire" is toilet, convenience stores are "konbini". "Eki" (train station), "sen" (line), "densha" (train). "Doko" means where; use a noun and doko in combination to get directions (your grammar will be bad, but that's fine). "Kirei na" (clean, pretty), "umai" (nice), "sugoi" (amazing). Ohayo "o-hai-yo" is good morning (add a gozaimasu for more formality), "konbanwa" is good evening.