Welcome, Vas!
Here’s some basic info on getting to the JMT. I’m assuming you’ll start in Yosemite (most do).
Reno, Nevada is one of the easiest airports to access the JMT from. The Eastern Sierra Transit bus stops at the airport and will bring you to Lee Vinning, Mammoth Lakes or Lone Pine, CA. From Lee Vinning or Mammoth Lakes, you can transfer to YARTS for your connection to the northern terminus of the JMT.
San Francisco, Sacramento, Oakland, Fresno and Las Vegas all provide reasonable access to the John Muir Trail as well. From California, you will take a taxi to Amtrak to YARTS (in Merced) or a taxi to Greyhound or Amtrak and then on to connect with Eastern Sierra Transit (in Reno).
Source: PCTA.org