How did they get the moon buggy on the moon?

Answer 1

The lunar rover came to the moon onboard the LM (lunar module) it was stowed in a small compartment and deployed thusly...

quoth the wiki

"Deployment of the LRV from the LM quad 1 by the astronauts was achieved with a system of pulleys and braked reels using ropes and cloth tapes. The rover was folded and stored in quad 1 with the underside of the chassis facing out. One astronaut would climb the egress ladder on the LM and release the rover, which would then be slowly tilted out by the second astronaut on the ground through the use of reels and tapes. As the rover was let down from the bay most of the deployment was automatic. The rear wheels folded out and locked in place and when they touched the ground the front of the rover could be unfolded, the wheels deployed, and the entire frame let down to the surface by pulleys. The rover components locked into place upon opening. Cabling, pins and tripods would then be removed and the seats and footrests raised. After switching on all the electronics the vehicle was ready to back away from the LM."

Answer 2

The Apollo lunar rovers, popularly known as moon buggies, were carried to the moon's surface aboard the Apollo 15, 16, and 17 missions. They were housed in the Lunar Module (LM) and then deployed once the astronauts landed on the moon. The rovers were designed to fold up in a compact manner to fit within the limited space of the LM.