The popular rule of thumb is two consecutive quarters of falling GDP. The actual US definition belongs to the National Bureau of Economic Research, which weighs employment, income, production and spending, and which has declared recessions that did not fit the rule and declined to declare ones that did.
Dating is retrospective by design. The committee typically announces a start date six to eighteen months after the fact, so an economy can be well into a recession, or already out of one, before it is officially in one.
Equity markets do not wait. They price the contraction in advance and typically bottom while the data is still deteriorating, which is why the worst headlines and the best entry points tend to arrive together.