There are two major airports near Berkeley, San Fransisco international airport (SFO) and Oakland international airport (OAK).
Unless you arrive at odd hours, the simplest way to get to Berkeley from either airport is taking the BART (Bay Area Rapid Transit). Looking at the SFO map, the BART station is next to the International Terminal G (sometimes JetBlue) and a couple of minute walk from Terminal 3 (United), otherwise take the free AirTrain to BART (runs every few minutes). The BART takes 55min and costs $10.70 each way (as of 2023), it’s every 15min during the day, every 20min at nights and weekends. Tickets can be purchased at any BART station; hold on to it as it’s needed to exit. At SFO, take the Richmond line directly to the Downtown Berkeley stop, or take Pittsburg/Bay Point or Antioch train to the 19th St. Oakland station, were you can transfer to the Richmond train to the Downtown Berkeley station. (The trains usually wait for each other at this station, except when one of them is delayed.)
From OAK airport, you can also take BART ($9.60 each way); the station is located across from the Terminal 1 baggage claim area and a short walk from Terminal 2. Change at Oakland Coliseum to the Richmond train, and take that to Downtown Berkeley.
A taxi from SFO to Berkeley will probably cost around $100. An Uber car around 60. Driving times vary between 35 minutes (no traffic, very rare) to well over 1h15 (traffic jam on bay bridge, quite common). Street parking in downtown Berkeley is difficult and often limited to 2h. For this reason, the use of a rental car is not encouraged.
