Golly, how long is a piece of string?
First you would need to look at the dozens of different kinds of teaching situations from part-time work in High Street evening and and cram schools, to full-time in mainstream primary and secondary schools, to universities, and in-house corporate teaching . mainstream schools usually offer a contract for a full academic year, but be aware that the long holiday might not be salaried although you may be contracted to come back and do the second semester. Regular schools will sometimes employ for just one full semester.
Cram and evening/weekend schools will often offer part-time work on the basis of you accepting to teach a complete course module, usually of around 30 hours, but this may be just one two-hour lesson a week. Once you're in there teaching on one course, you may get offered more as other courses start.