Los Angeles is known for its car culture and for good reason: for anything other than local travel, public transportation here generally isn't very good. The Metro Rail system is 98.5 miles (158.5 km), which is paltry when compared to New York City's 660 miles of subway lines. Unless you live a short walk or drive from a station and work close to a station, using the train for your commute won't be very practical.
The Metro Bus system is more robust, with 170 bus routes covering nearly 16,000 stops and 1,433 square miles (3,711 sq km). Most neighborhoods have good access to bus routes. But if you're going more than a few neighborhoods away, it's a slow method of transit: you'll sit in the same traffic everyone else does and it's made worse by the fact that the bus is frequently stopping to pick up and drop off riders. The city is working to establish more express lanes for buses, but until they're common it will continue to be a slow way to travel.
The bottom line is you can survive in LA without a car, but your life will be more complicated and you'll spend a lot more time commuting and running errands. Plus, LA has a lot to offer on the weekends: hundreds of hiking trails in its mountains, miles of great beaches, easy access to great weekend trips like Palm Springs, Santa Barbara, and Joshua Tree National Park. You'll need a set of wheels to properly explore all of it.
TRANSIT & WALKABILITY NEIGHBORHOOD RATINGS
For each Los Angeles neighborhood you'll see a Transit rating and a Walkability rating. The Transit rating tells you how good and reliable public transportation options are in that neighborhood. The Walkability rating tells you how many local amenities (shops, restaurants, fitness options, etc.) you can walk to in that neighborhood.