How you're doing
The small-talk status words for checking in and making plans: well, busy, free.
genki
polite genki desuwell, energetic, healthy
元気 げんき 元気です
The check-in word ('genki?' = how are you doing?) for someone you haven't seen in a while; it also describes good health, good spirits and lively people.
hisashiburi, genki datta?
Long time no see. How have you been?
久しぶり、元気だった？
ohisashiburi desu. ogenki deshita ka?
It's been a long time. How have you been?
お久しぶりです。お元気でしたか？
When you ask about someone else politely, add o- (ogenki desu ka?); about yourself it stays genki desu.
isogashii
polite isogashii desubusy
忙しい いそがしい 忙しいです
Says a person is busy; it is the standard small-talk status (saikin isogashii) and the polite excuse for turning something down.
ashita no yoru, isogashii?
Are you busy tomorrow night?
明日の夜、忙しい？
ashita no yoru wa oisogashii desu ka?
Are you busy tomorrow evening?
明日の夜はお忙しいですか？
Describes people, days and workplaces (kyou wa isogashii, isogashii jiki), but not a crowded street: that is hito ga ooi or konderu. Asking about someone else politely, add o-: oisogashii desu ka? The opener oisogashii tokoro sumimasen = sorry to bother you when you're busy.
Learn alongside: hima
hima
polite hima desufree, bored, idle
暇 ひま 暇です
Says someone has free time ('hima?' is the standard opener before an invitation) or is bored with nothing to do (hima da naa).
ashita no yoru, hima?
Are you free tomorrow night?
明日の夜、暇？
ashita no yoru nara hima desu yo
If it's tomorrow night, I'm free.
明日の夜なら暇ですよ
Asking a coworker, clerk or stranger 'hima desu ka?' can sound like 'got nothing to do?'. To ask politely, say ashita no yoru, aitemasu ka? or jikan arimasu ka?; hima desu is fine about yourself.