Wow, this thread took off after I went to sleep!
"ashita" (明日) means 'tomorrow', as Monger mentioned. The characters literally mean "bright day/sun", and they are not used phonetically, so you can't pronounce each individual character in the compound; they are pronounced as a unit.
Verbs
present polite ending = -masu
past polite ending = -mashita
examples:
'go' = ikimasu; 'went' = ikimashita
'do' = shimasu; 'did' = shimashita
'eat' = tabemasu; 'ate' = tabemashita
As I mentioned in my last post, the tense you choose in Japanese doesn't always match the one you'd use in English! So saying "wakarimasu" instead of "wakarimashita" is a definite sign of a foreigner!
Names
'Yamashita' (山下)literally means 'under/below/bottom of the mountain', but it really means 'at the foot of the mountain'. A lot of Japanese family names are geographic in nature, so you can imagine why Yamashita is such a common surname. That's where a lot of people live!
Other common names:
Suzuki (鈴木)= literally "bell tree"
Yamada (山田)= "mountain field"
Satoh (佐藤) = literally "help wisteria", used phonetically
And my wife's family name (and also the name of a prefecture in Japan) is
Yamanashi (山梨) = "mountain pear"
If you ever see Japanese pears ("nashi") in the grocery store, try one! They're delicious.
Characters
For anyone interested, here are some basic characters:
山 - yama - mountain
人 - hito - person
田 - ta/da - field
川 - kawa - river
力 - chikara - power
男 - otoko - man (notice it's a combination of 田 and 力)
女 - onna - woman
日 - hi - day/sun (you can call the sun o-hi-sama, literally "honorable sun")
月 - tsuki - moon
And if you ever watch anime and have seen Ultimate Muscle, or Kinnikuman, or what ever it's called, Kid Muscle has a glowing character on his forehead 肉, that literally means "meat", but is part of the compound kinniku 筋肉 ("tendon meat") which means "muscle".