Most travellers reach Jerusalem by bus or train from Tel Aviv, or by bus or sherut (shared taxi) from Ben Gurion Airport. It's also possible, though time-consuming, to cross overland from Jordan across the Allenby (King Hussein) Bridge.
The best price found from United States to Jerusalem is on September 26th, 2018, travelling with WOW air. See more options, compare prices and book: search flights.
Jerusalem's Old City is walkable and the rest of its neighbourhoods are well connected by buses and a reliable light-rail system. Metered taxis can fill in any gaps. Car hire isn't required if you plan to limit your travel to the wider metropolitan area, but it's an efficient way to day-trip to the Judean Hills.