Domo Arigato
The phrase "doumo arigatou gozaimashita" is pretty easy to explain.
It basically just means: "Thank you very much."
In this case, I'd put the definitions down as:
Doumo = thanks
Arigatou = thanks (yes, again. We're a redundant sort)
Gozaimashita = for something that has happened
It's pronounced, more or less,
dou mo ari ga tou go zai ma shi ta
If you're speaking to someone who is your equal or "lower" on the hierarchy, you
can just say "arigatou"
or "doumo" (although just saying "doumo" is more on the terse side of
things (and can be taken as being
a bit rude)) to mean, basically, "thanks."
For people "above" you in the hierarchy (e.g. sensei, sempai), you would usually
say the full phrase. If
you're going to drop something out of the phrase itself, I would probably drop the
"doumo" part and just
say "arigatou gozaimashita" to someone.
Note: The Japanese "r" is not really a "liquid r" with the tongue
curled back (we don't have that
Amerrrrican Arrrr (as in "Arr, matey!") in our phonetic system), but is more
akin to the "l" sound like in
"lollipop." My Japanese "r" is somewhere between an "l" and
a "d" -- it's like an "l" but more like a "stop"
consonant than a liquid (although it still is a liquid).
-- by J. Akiyama