Where you are going, and when
Start from the home page or from the bar along the top of any results page. You need a place to leave from, a place to go, and a date.
The two place fields are lists, not boxes that guess. Every airport with a departure is in them, along with the cities that hold more than one, and the whole list ships with the page — so typing filters it as fast as you can type, with nothing asked of the server in between. Pick the city entry when you do not mind which of its airports you use.
The calendar prices its days
Open the date field and each day carries the cheapest fare found for it. That is the point of it: the gap between a Tuesday and the Saturday beside it is often wider than anything else you could change about the trip, and it is much easier to see than to guess.
Everyone travelling, from the start
Set the travellers before you search rather than after. A child takes a seat of their own and pays a reduced share of the adult fare; an infant travels on an adult's lap and pays a smaller share again. Because they cost different amounts, a price found for one adult tells you very little about the price for a family — and the picker will not let you past the seat limit it enforces, so it is better to hit that here than at checkout. See Flying with children.
Cabin is chosen here too.
Reading the results
Every result says what its fare allows in six lines — personal item, carry-on bag, checked bag, changes, cancellation and seat choice — before you fill anything in. Two flights an hour apart at the same price are often not the same offer at all, and those six lines are where the difference is. See Baggage for what each one means.
Above the results are tabs that reorder them: Best to begin with, then Cheapest, Fastest, earliest out or in, and shortest layovers.
Narrowing it down
The filters sit beside the results and cover rather more than price: layovers and the conditions attached to them, travel time, flight times, arrival date, airline, aircraft, and which airports you pass through or use at either end.
On a return trip each leg filters separately, so a morning outbound and an evening flight home is one search rather than two.