1. depending on
after a noun
この答え次第で、大きな問題になる可能性がある。Depending on this answer, it could become a major problem.
2. as soon as; immediately after; upon
after a noun or the -masu stem of a verb
都合がわかり次第、連絡をください。Please contact me as soon as you know your availability.
3. as (e.g. "as one is told", "as one wishes"); whatever (e.g. "whatever is at hand")
after the -masu stem of a verb
4. order; program; programme; precedence
5. circumstances; course of events; state of things
6. reason
こういう次第で、遅くなりました。This is the reason I am late.